Ok, so it appears that they chopped a .22 rifle and stuck on a handgun stock. Nothing new or groundbreaking there.
If the best you can do is 3-4 inch groups at 30yds (and assuming its not you) then there is something wrong with the gun or the scope.
I can do that well or better(usually) offhand with a number of .22 pistols. And my Contender in .22LR is waay more accurate than that.
Several comments on the XP-100. After a long time, I finally found one in original condition (the mid grip plastic stock, vent rib, etc). The gun wears a Herter's 2x scope and is ...rather accurate.
Unlike some (apparently) the trigger on mine is one of the best I've ever had on any gun. Light, crisp, no overtravel, just overall sweet.
For a long time I couldn't figure out why Remington created the .221 Fireball round. Other than making it so that you had to buy Remington ammo, why not just chamber the gun in .222? Or .223?
The answer turned out to be the XP-100 itself. It had a 10 inch barrel. The .221 Fireball case is the optimum size to get the max performance out of that barrel length. Shooting a .222 (or larger case) from a 10" barrel only burns more powder for no significant gain in velocity. The .221 will get more speed from a rifle length barrel (everything does), but from the 10" the only thing a .222 did was burn 2-3gr more powder for the same speed.
There was a semi auto .221 that used a 30 rnd mag. They were made for a short time (not by Rem), although I can no longer remember who made them, or exactly what it was named (Bushmaster or Imp are running through my head, but either might be wrong). It was a bullpup style, "handgun", the pistol grip would swivel for either left or right hand shooting, and the action lay along your forearm. I think it might have been intended as an aircrew survival weapon, but if so, the military never took more than a glance at it.