If a gun of mine came back from a tuner like that, at bare minimum I'd want my money back. Just so I'm clear: it did this across two different regs over the course of several years and multiple tuners have observed this issue and been unable to resolve it? I realize there are a lot of specifics in that sentence but let me break down a few things.
First off, an airgun is a complex system. Whenever possible, when doing diagnostics, the name of the game is to try and eliminate systems to isolate the cause. And in the case of remote diagnostics, it tends to be a probability game. I can't guarantee any one observation isn't a fluke or what have you, but odds are it isn't. Having worked in pneumatic (and other) complex systems diagnostics for years now, generally if you assume any observation is a fluke for your hypothesis to work, you'll end up being wrong.
So I say multiple regs over the course of years because if it is two regs, I'm going to guess the problem isn't the reg sticking. That two regs would stick in an identical way strikes me as unlikely. One possibility here though is that, if the gun never got that much use under either reg, neither broke in and so they just fill slowly and you're cracking off shots fast over the chrono and you'll occasionally get a partial fill. If you're shooting fast, it'd also explain why, flier aside, your numbers look like poop. I see an 820 something in there and a max of 873, and your STDev is 20 so thats pretty lousy.
So pressure is one possibility.
Another possibility is the moving mass system. Again checked and polished though makes me think that is unlikely.
There is tune, and you alluded to this that the gun would need to be run at higher power for accuracy. So there is something to this, at least half of something. Velocity, twist rate, and pellet design are all related. A gun doesn't NEED to be run at high power for velocity consistency alone though, it is a game of balance between reg pressure and hammer power, so going down to 25 foot pounds from the ~30 the gun was meant to be run at shouldn't cause this kind of velocity issue if tuned right. And again, a good tuner should know this.
A final possibility I'll throw out there is the barrel. Something, maybe pellet head diameter consistency issues, maybe barrel fouling, maybe just a bad barrel, something in there. It is hard to imagine this kind of issue coming from the barrel alone, but something in that system perhaps. Clipping and other shroud issues are possibly at play here as well.
The final thing that really bakes my noodle is that none of the tuners you sent it do "noticed" this. I find that hard to believe. No tuner worth their salt would tune a gun without a chrono, and even the occasional power drop aside that shot string is abysmal. No offense intended, but this makes me think the problem what in the firearms industry we call an "operator headspacing issue." Other than a bad tin of pellets though, my best guess for how you could cause this yourself is simply cycling the gun too fast for the reg to be refilling. *shrug* I will watch this thread with some interest though, because this is a real puzzle and I want to know what the cause ultimately is.
I hope something in this wall of crawling ants was useful. :/