I have a HW97, so not exactly apples to apples, but "my" gun prefers h&n ftt's. They fit very well. If most pellets fit your leade loosely, I have found H&N Baracuda Hunter pellets, both the older "10.3gr" and newer labeled 10.5gr to be the most consistently snug in fitment (about the largest head size in .177) and may be worth a try.My gun also prefers to be rested on the schnabel (Lol), but if shooting off hand just behind the stock screws works well, or palm up in front of trigger guard, depending on my position. While benched I have purposely adjusted my holds and watched POI changes at 40 yards, something you could try out and see what's best for you and your gun.If all else fails, it could be some mechanical or barrel issue. I know my HW95 took a long while of casual shooting to settle in and get some decent accuracy, don't know how many rounds you have through the gun yet. Hopefully things come together for you soon.
I agree nothing beats a breakbarrel when it comes to cocking and loading speed and foolproofness. However, the "arm-waving" factor of breakbarrels vs. underlevers is not anything to base a weapon choice on. With an average-size breakbarrel, the shooter needs to raise his hand to the height of his hairline, or higher, then bring the hand down in a wide, forceful arc. It's like waving your arm to raise attention, while trying to stay undetected! An underlever needs no wider or longer arc of motion to cock than a breakbarrel, while a sidelever is definitely stealthier than either, since the shooter doesn't need to raise his cocking hand anywhere near the muzzle to cock the gun, and a sidelever can be cocked and loaded even prone.