First, let me say this is a fascinating discussion! Its gone a bit afield, but really interesting. Btw, 'Black Bessie' was salvaged off a battlefield and hidden, iirc, not placed in a cache to repair and serve after the occupation.
none of the canon universe makes sense from just about any perspective you choose, just do what you want.
Also, Reading the previous posts, I have several points of agreement, mostly this one. Its a game, after all. The designers focused on massive wars, political intrigue, and not the little guys off in the corners without the bucket, to, you know, after shafting them. ^-^
And they didn't concentrate on the clever, or even commonsense, with notable exceptions (truly massive doses of stupid pills, here). Yes, they had holdout military reserves - iirc, according to the ISP 3 section mentioned, those were used (if they ever really existed - I despise the ISP books simply for that, as well as the Genecaste TP) with the exception of the crippled TDF WarShip in mothballs resurrected by the Blakists in the Jihad for the Concordat. (I suppose the biggest remaining golden eggs are the Amaris storehouses supposedly hidden in the deep Periphery - good luck finding them, eh?)
Anyway, I think equipment and materials caches such as the Amaris factories or Marion Hegemony's Germainium storehouses make a LOT more sense - rebuilding materials and military production equipment or stockpiles would go a long way to quickly bouncing back - but it wouldn't be easy to hide in the kind of quantities needed. Massive quantities, by the way. Massive - huge - in scattered locations, or a couple remote locations guaranteed to be secure for decades. My point is they would have been forced to consider a member planet or nearby system, since just moving it would have been next to impossible while facing occupation. Something like the collapse of Nazi germany might make sense, as individuals move to deny things to the invading Star League that they could loot for their immediate benefit. Any number of them could still exist, similar to the storehouse for the Helm memory core.
But a technology cache? ...Not really. The C* 'Holy Shroud' campaign (more than one, according to the fluff) was a pretty cunning bit of in-universe explaination, and went a long way toward making an extended SW timeline plausable. Sure, there are all kinds of tech companies, universities, colleges, hobbists even, but the kinds of massive government programs to recover some of these things and the SW themselves would work to keep the number of Bill Gates/Steve Jobs down. In-universe, they stand out, and the whackos in the white bathrobes would have been on them like cheap lawyers on a wrongful death suit. When the SL took education materials, books, equipment, EVERYTHING the Concordat needed to recover after they won, it was the only smart thing they could have done.
Frankly, the idea of the Helm, Dallas, and the SL-era Prometheus data core were drivers to explain new rulebooks and TROs, imo - it was the only thing that could explain how after only a few years could go by such massive improvements were possible, but I use the possibility of a SL Prometheus database to explain the conditions of my AU. Its your fanfic or AU, after all. Oh - seems to me there was a fanfic here where an operational WS misjumped and came out in 3025 with such a memory core - it was pretty good. Looking forward to reading your take on it.