I agree, go with the .45-70. I don't remember anyone here having serious accuracy issues with them. I bang flopped a year and a half old buck at 220 yards, with my Handi, a .45-70, 325 gr. Hornady LE, and a "Hail Mary" next to the last day of our season. They all worked together. I agree with Ty, shoot 'em and learn 'em. The Handi with LEs is NOT just a 100 yard rifle, and it, the Handi .45-70, will take anything in North America. Ammo is readily available in a wide range of loads. It's not cheap, but it doesn't wipe out your budget either.
Good luck, Good Shooting,
Pete