I can't fairly represent the FAA's point of view here.
I'm not saying that to be cagey; I just haven't spent tons of time thinking about all of the "what could go wrong?" and "why is airplane certification done the way it's done?" It's easy to sit on the outside and say "that's ridiculously overly conservative!" but I suspect the truth is there is a mix of over-conservative and genuine purpose to "until you prove it via certification, it's not certified as true".
Air-cooled engines have wildly varying operating conditions. Airplanes need to take off not just on a 60ºF sea-level departure to a 3000' cruise, but also at a 105ºF departure from 5000' with a direct climb over terrain to 15K feet. The fuel will sometimes be 125ºF after baking in a tank or a wing all day. It might not be on the exact centerline of the specification range. It might be 6 months old and some of the higher volatility compounds present in reduced amounts. High-strung turbo engines with fixed timing live with pretty low detonation margins, especially at partial mixture settings. Pilots rely on the pilot-operating-handbook or airplane-flight-manual for performance calculations with regards to runway utilization, accelerate-stop/accelerate-go distances, all engine climb gradient and one-engine-INOP climb gradient. Any amount of performance degradation that would invalidate those figures is cause for FAA rejection of the STC. Having flown a handful of heavy, hot, and high departures where the ground isn't falling away from the airplane nearly as quickly as I'd like, I can appreciate a certain amount of conservatism here.
So, I have to give the FAA some benefit of the doubt as I'm not an expert on certification topics. I do believe in the technical ability and already completed lab, bench, and flight testing that GAMI has done and the way they've set out to approach the problem, but to be fair and balanced, they've done some amount of "we think the FAA/PAFI process is fundamentally the wrong approach and we're going to go about it this other way that we think is superior." I happen to think they're right, but when you very publicly do that to a government agency who said they want the process to work this other way and you don't participate in their preferred process, I think it's reasonable to expect that you'll run into delays. (Even if no FAA person is acting in the least bit unethically; you're just trying to use a different process than the one they're putting their energy into and even if everyone has the best intentions, that will cause friction and slowdowns.)