First 4 shots after Fill go wild

No guys, an Air Venturi Avenger is a 300 Bar fill gun. 4,000 is a bit conservative.

My 25 caliber does not do this but I've noticed over several shot strings that the velocity variation of some of them is > 30 fps. Not great. But that should not cause "wild" shots.

Is it possible the barrel is inadvertantly bumped in the fill process? The Avenger barrel is not supported at the muzzle end, it has a support at the action and about 2/3 of the way up but not at the muzzle. My DonnyFL adapter and the printed moderator I am currently using support the end of the barrel. That might be something to try. Just being extra carefull about the way the gun is handled during the next fill would also be something to try - that costs nothing.
 
I’ve found point of impact change to be a common problem. Seems like any change no matter how slight will have an affect. Typically a minor one but often just enough to cause a miss at long yardages. Air rifles are more susceptible then power burners in my experience and I think the main causes are pellet variables, barrel to action attachment issues and often just condition changes we don’t notice. I find I have to “sight in” each and every time and then watch for condition changes. As a result of all of this for me air guns are limited to 75 yards in hunting situations. Unless I would have unlimited targets which is extremely rare. Air guns are hard to shoot for extreme accuracy. We’re all stretching out the ranges and as a result testing the equipment and ourselves to the maximum. I read often on the forum of fellows shooting 200 to 300 yards with guns really designed for 50 to 75 shooting.
 
I'm not surprised, you are overfilling it by 1,000 psi!

You might want to look into the avenger. Its a 300 bar fill gun. So how is 4000 psi over fill? Don't confuse avenger with a marauder. 300 bar is 4350 psi. So the avenger is fillable to over 4000 psi.

What the OP is experiencing is reg creep. Happens even on a $2000 fx impact. The first 2 to 3 shot will be low and poi will differ. It's always good to dry fire 2 to 3 shots before going out hunting.