Hi Dinny,
Several years ago I was deer hunting with a traditional style muzzleloader. I was on the ground still hunting when a coyote ran past me at about 10 feet. The 'yote traveled 15 yards, stopped and laid down to watch something. When I fired, I lost sight of it, but knew where the yote had been. I walked straight there to a not quite dead coyote, with an empty gun. So since then all single shots are backed up with a revolver. So if you switch to carrying a Handi, bring a wheel gun for your hip, .38 SPCL would be minimum. Since you have a .45 Handi, a Ruger Blackhawk in .45 Colt would get my vote.
As for the 870, I shoot cylinder bore so I don't have to worry about changing chokes for different loads. Load your own and you can control the pattern better than with choke tubes. For tighter patterns use heavy shot cups (stiff) for the ultimate long range pattern get the shot cups that are not pre cut, or tape them so that it is harder to open.