Locating new Manticoran shipyards
On the subject of building shipyards outside the Manticore System. The SKM isn't going to be building any major naval shipyards outside the Home System for the foreseeable future. There are several reasons for this.
(A) All of the Star Kingdom's major industry, resource extraction, and general infrastructure are located in the Manticore System. The expense, in terms of money, shipping, and manpower in building up a major shipbuilding node someplace else, like Grendelsbane, is totally out of the question at this moment, if only because of concerns about industrial rationalization.
(B) The Manticore System is the most heavily defended point in the entire SKM, including (especially) its newest annexations. Ships being built at Manticore have the highest probability of surviving the construction process.
(C) In association with (B), above, the Manticore System is already the critical defensive commitment of the Star Kingdom, and, arguably, of the entire Alliance. If the Home System goes, the war is over. There's no tomorrow if the Manticore System goes down, whether it's occupied or not. Occupation would be even worse, because it would involve the total neutralization of the Wormhole Junction, rather than simply the destruction of the centuries worth of supporting infrastructure built up to service the Junction, but a simple raid which destroyed Manticore's orbital industry, or even left a sizable portion of that industry intact but destroyed all of the ships building in the dispersed yards, would be totally decisive. Which is precisely what Theisman was thinking when he organized Operation Beatrice. Since this system absolutely must be held, and since that is going to mean that the Alliance has to station sufficient strength there to defend it, and since it's imperative to avoid dispersing their available mobile strength defending other possible targets which aren't absolutely essential, the Manticoran Admiralty and Government are both firmly of the opinion that investing the resources and manpower in a major shipyard somewhere else would be not simply foolish, but a recipe for disaster.
(D) In regards to the possibility of placing a major shipyard in the Talbott Cluster because it would be so far away from Haven that, like the Andermani, it would be protected by its sheer distance from anyone who wanted to attack it, again, it's not going to happen. While there is a great deal of superficial appeal to placing a major yard there, that appeal is found primarily by focusing with absolute tunnel vision on the threat of Haven, which no one in Manticore is likely to be doing after what happened at Monica. Shipyards in the Talbott Cluster are going to be much more exposed to attack by Solarian forces than shipyards at Manticore, or even in Silesia. And, at the moment, everyone in the Star Kingdom -- as I think Honor's reflections have made clear -- is still uncertain about which way the League is ultimately going to jump over the Talbott Cluster. That being the case, putting a major shipyard into the area does several undesirable things from Manticore's perspective. Among other things (in other words, this isn't an exhaustive list), there's the issue of the very heavy cost to start up a military-grade shipyard in such an area. There's the exposure to the "Solarian threat," which recent events in Monica suggest is not insignificant. There's the fact that building a major shipyard in the Talbott Cluster could clearly be viewed as a provocation by OFS, which might actually increase the chance of Verrochio finding the testicular fortitude to try again. There's the fact that with the sole exception of the systems of the Rembrandt Trade Union, there's no place in the Cluster that has a starting point as advanced even as that of pre-Alliance Grayson, so we are talking about the need to transfer not simply financial and physical hardware type resources into the Cluster, but also the necessity of transferring scarce, expensive, highly trained technicians who would just happen to be the very sorts of people someone like Mesa/Manpower or their buddies in Technodyne would like to get their hands on.
(E) As for building a major shipyard at Lynx itself, that's an even worse idea. The Lynx System is not directly associated with the Lynx Terminus, despite the nomenclature adopted. They are several light years apart. So to take advantage of the population of the Lynx System (who aren't really trained up to the necessary standard of technology to begin with), you would have to transport them to artificial habitats in the same system as the Lynx Terminus. And while it's true that that shipyard would be on the far side of the Junction, and thus a long way away from Haven through normal-space, it's not far enough away through the Junction. If the Havenites take out the Junction defenses, there's nothing at all to prevent them from launching attacks through the Lynx Terminus to take out the shipyards being built there. And there's no point in putting a shipyard in the same system as the Lynx Terminus, or for that matter in the Lynx System itself, simply to service the Cluster. Why? Because ships can be deployed there from shipyards in the Home System with no time delays at all. So why build a major yard out from under your primary defensive umbrella if there's no deployment advantage and you're facing such an uphill struggle to get the personnel, the technology, and the resources you need into the desired star system in the first place?
(F) But what about depleting the resources in the Home System? That's not going to happen any time in the next, oh, century or four. A star system is a great, big place, especially given the capabilities of Honorverse-era technology. The raw materials that an Honorverse extraction center needs to produce the components which go into Honorverse warships can be extracted from a huge number of sources, including asteroids. And even given the size of the ships built in the Honorverse, the resource base provided by an entire star system to a society which can generate gravity, or counter-gravity, at will is literally incalculable. It might become a problem eventually, but not until they finished using up not only the asteroid belts of both components of the binary star system, but also the moons of the various planets. So the question of basic resources is a moot point, except inasmuch as the extraction industry required to make the most efficient possible use of the resource base is already in place in the Home System and would have to be built from scratch someplace else.
(G) In association with (D), (E), and (F), there's the fact that Manticore is where the Star Kingdom is positioned to get the maximum economies of scale out of its construction projects. It's the natural center of the Star Kingdom's financial and industrial muscle, and keeping its major shipbuilding efforts there allows the maximum flexibility in the application of that industrial and financial power. In effect, Manticore is mass-producing superdreadnoughts the same way that Kaiser mass-produced escort carriers during World War II, and it would be very difficult to attain those same types of economy of effort in a yard built out back of beyond without all of the various support structures already existing in the Home System.
(H) It's been argued that putting a major shipyard into the Talbott Cluster, for example, would not in fact add to the Star Kingdom's defensive commitments, since the Navy is obligated to "die in defense" of the Star Kingdom's planets. This is an incorrect view. While it is true that the Star Kingdom has a moral responsibility to protect its member planets and their populations, two other points are also true. First, without the presence of a major strategic target, most of the star systems in the Talbott Cluster or Silesia wouldn't be objects for attack. That's somewhat less true in the case of the Talbott Cluster than it is of Silesia, of course, since Mesa/Manpower and Commissioner Verrochio are both bound to regard any Manticoran presence in the Cluster as a long-term strategic threat to their own security and/or freedom of operation. Nonetheless, the presence of a major Manticoran shipyard, with both its potential threat value and the seductive value of an opportunity to possibly get one's hands on not simply specimens of Manticoran hardware, but of Manticoran technicians and specialists who know how that hardware is put together, would enormously increase the probability of their taking prophylactic action against the system where the yard was to be located. Second, while the Star Kingdom's military has a moral obligation to defend all of the Star Kingdom's planets and citizens, it's overriding responsibility is to win the war, preserve the Star Kingdom as an entity, and, if necessary, to subsequently liberate star systems which may have fallen into enemy hands. If abandoning Trevor's Star to the present Republic of Haven allowed the Home System to be held, and the Apollo-equipped ships building there to be completed and commissioned, then even the citizens of Trevor's Star would argue that the only sane thing for Manticore to do would be to abandon them and plan on coming back to liberate them later. Even against an opponent who was going to nuke planets, a squadron or task force which would ultimately be unable to prevent the attack from going through, would arguably be criminally remiss to stand and fight to its own destruction. Those ships would be of far greater value to the Star Kingdom as part of the navy fighting to prevent the same thing from happening to Manticore, Sphinx, Gryphon, and all of the other recent additions to the Star Kingdom, then they would be as drifting debris in orbit around a planet that they'd never had a hope of saving in the first place. The sacrifice of a light squadron, or a flotilla might be justified on the basis of the political and morale damage of abandoning an inhabited planet without a fight, but even there, you would get into the moral question of the flotilla's CO's responsibility to his own personnel to see to it that they didn't die uselessly.
(I) Also, I believe that someone has argued that, ultimately, no one can hope to hold any star system in the face of a powerful attack. That simply isn't true. The corollary to the "no one can hope to hold any star system" which holds that all the defender can realistically do if the bad guys decide to concentrate enough force against them is to make the attackers bleed has a greater degree of validity, but the correct argument (which I believe you also put forward, Mike [g]) is that the defenders' objective is to make the cost of attacking such a system or target prohibitively high. However, the point that I think you are missing, Mike, is that it is entirely possible to make the cost "too high" by making that cost "equal to every single ship in your entire navy, plus one." For example, if (and I'm not saying that this will happen) the Manties are able to get a system-wide Apollo network set up to cover the Home System, then back it up with another 60 or 70 Apollo-capable SD(P)s, lavishly equipped with system surveillance arrays and FTL reconnaissance assets, and then add in a few dozen thousand LACs, the "too high a cost" to take the system out would be more than the entire Havenite Navy. Which equates to their ability to hold the system in the face of any attack which could be launched against it. And, for that matter, with those defenses in place, Manticore could hold off the entire active strength of the SLN, as well. Probably more easily than they could hold off Haven.