Load the .38 with Glasers Saftey slugs if you can find them, or Federal Premium Guard Dog ammo. Both are designed to prevent over penetration.
Another option you might consider is a Magnum Turkey load. Load the 500 with a magnum turkey load of 4's or 5's, put a full choke in and rest easy. As far as recoil goes, there are not many loads out there that recoil more than a 12 gauge turkey load, but I have killed alot of turkeys and do not remember any recoil, and I shoot an 835 with a 3 1/2", 2 ounce load of 5's. Adrenalin is a wonderful thing. At 10 yds, expect a pattern about 12" - 18" wide, if that.
Winchester 3" turkey loads run about 1300 fps at the muzzle. They have 1 3/4 ounce of either #4, #5, or #6 shot in them.
My HD shotgun for years was a Mossy 500 with a 20" turkey barrel, a full choke, and loaded with Winchester Supreme XX Magnum anti-turkey loads and never for a minute felt under gunned.
As always, be aware of your background, but with the scenario you described, you should be fine.