Would you rather have a rare design you have few spare parts for filling out a garrison cluster, or parts like engines, myomer, weapons, electronics, etc, to bring a frontline design back up and bringing more worlds under your power?
As noted before, the engine, weapons, internal structure, armor, and electronics (TAG in particular, but the internal computers are going to be a pain, I guarantee it) are all incompatible with Clan front line machines because they're a different tech base. The sinks are less of an issue for that reason - SHS are pretty similar from what we can tell - but the engine differences are going to cause trouble there and very, very few Clan front line machines, if any, use single heat sinks anyway. The only thing there that's possibly adaptable without causing a major headache is the myomer bundles, parts of the jump jets, and maybe pieces of the cockpit. Yes, it's possible to get around that, but it takes a lot of time and effort, and you're depriving yourself of a perfectly functional 'Mech to create something that's going to be a maintenance headache and very, very likely break the Omni functionality in the process.
What they're going to strip to get front line machines operational are likely the garrison cluster's
technicians and second-line Clan BattleMechs, not Star League hardware.
Guess this is a a good place as any to lament again that Klondike didn't mention the Sling was also built on Victoria or give us the chance to find out Shengli Arm's Star League era name :(
Unless Shengli Arms' facilities were originally part of Mountain Wolf BattleMechs and in the Lyran Commonwealth, it's apparently not compatible with the background we were given. Now, whether or not that would have tied the loose ends up is another issue, but there may have been information I'm not aware of that pointed another way.
If you're willing to squint
just right, though, Mountain Wolf could have had facilities there but still have been
headquartered in the Lyran Commonwealth. Multinationals were pretty common in the Star League era, after all, and we know Barbara Liao was supportive of Kerensky, so if it works for your game, it's not completely implausible at all. Just... odd.