The NE Handi Rifle is great if you keep it limited to what it's designed to do. I bought the slug gun version for $120 and find that when loaded with Win super X sabot slugs it can print 4" groups at 100 yards using a ghost ring sight. Slugs aren't know for accuracy but it's still perfect for what I need as I hunt in Illinois brush country where no shot is going to be longer than 100 yards. I've also found that it's accuracy doesn't differ too much if I shoot offhanded, I still get 6" groups at 100 yards.
I also bought the .50cal muzzleloader barrel for $75, the 12 ga 3 1/2 inch extra full choke turkey barrel for $55, and a 20 ga modified choke for small game for $35. So for $285 I got 4 different guns for 4 different uses. It's not the perfect gun but it does the job. With it I've taken 6 deer, 4 wild turkey's, loads of pheasant, ducks, geese, squirrels, rabbits and a lone coyote who got too close.
The 3" accuracy you found is good enough for almost all hunting. Only Varmint hunting and extreme long range hunting needs accuracy under a 1/2". You could probably ge that 1/2" accuracy with the .223 or .243 bull barrel as it is designed for accuracy.