Your situation is not uncommon. Even the best corvette shops will likely never see an LT5 engine let alone know how to work on it. From my perspective this is the one major issue that keeps the value of these cars down. The average non-technical owner simply can't find a reliable local shop to work on this engine.
The issue of the shop throwing parts at it is also not uncommon. As a matter of fact it's universal. The undisciplined technician wants to shortcut the process, make his money and move on to the next car.... and down the rabbit hole they (and your money) go. If you think about it this is not just a rare car, it's a rare engine. The average shop doesn't see one often enough to invest in the tools and learning to make it worth their while. That's why there are only a handful of shops around the country considered competent.
Your idea of going to a European specialist is not bad. Frankly and 80's 90's vintage Mercedes or Audi will share more similarities with an LT5 than a Porsche. I worked on them back in the day. That doesn't preclude the fact that a bad technician may try to throw parts at it. Try asking around who is the best diagnostician, talk to them, ask if they follow the factory diagnostics. Consider gifting them an FSM. They will certainly be more comfortable working on this engine than the local Vette shop that sees mostly SBC's.
Good luck,
H
