Accuracy problem with .177 FX Crown

A lot of great advise! One thing to add unless I missed it already, ok a couple of things, those flakes in my experience come from the pellets unless washed, most skirts carry a ton of production flakes, if they have been cleaned? Then areYou using a moderator and clipping? Mag alignment? Or make sure the ammo is the right one for the barrel? I know that’s standard work, but with 9 different Fx barrels, I am yet to see this leading up theory? But there is always new things to learn? And no production process is perfect! Hope you getter figured out👍🏻
 
Update... I received some H&N Barracuda Match pellets and they shot better than the JSB 10.34s. Still not great, but better. My groups were between .25 and .38" . I see Tom Gaylord is having the same results with the Dreamlite in his blog. Parts 3 and 4 describe almost the same results I have had.

https://www.pyramydair.com/blog/2019/07/fx-dreamlite-precharged-air-rifle-part-4/

I have never had to harmonically tune a rifle before, but I will give it a try over the next several evenings. I'm still not convinced that the barrel design is very good on these FX rifles. Just as a test, I let my finger touch the barrel while shooting. I touched it as lightly as I could, and the shot moved over an inch in 21 yards. That just seems wrong to me. I don't see how this can work well as anything but a target rifle. Any bumps in the field will move your point of aim, I think. 
 
I've wondered about the rigidity myself. The idea behind free-floating is that the barrel is allowed to resonate and flex freely so it is unaffected by any slight changes in fixture as well as disruption of resonance. So, I would expect poi to shift if it were touched. Harmonically balancing the hammer and reg will do nothing but help accuracy. I do a lot of experimenting with different wight pellets, different designs, and different diameters. Each gun has a sweet spot depending on the barrel and power setting. Balancing the valve and reg will reduce turbulence, boosting stability