Yes. Big slow bullets don't produce hydrostatic shock (bloodshot meat).

Once you get accustomed to limited range and hunt within that range, it becomes a challenge and less of a handicap.

A .45 colt 250-260 grain bullet will likely punch right through your deer. My 300 grain jhp's .458 bullets from my .458 Socom are moving out at about 1,800 Fps. They punch through bears at close range, under 20 yards. They'll lodge on the far side of bear and elk out past 60 yards.