RE: New England Handi rifle
Did you check the muzzle crown for any damage?
I personally don't like the cantlelever scope bases that those rifles use, the design doesn't lend it's self to great percision. Maybe you should lap your rings and still try another scope because 4"groups are pretty sad.
I would consider that rifle a challenge, a project for another day, but you may be right to get another gun for now if the season is upon you.