Thanks, guys. You've given me good advice. I think the Bushnell rifle scope makes a lot of sense, and so does the red dot. I've got a handgun red dot I could use. I never thought of using it on a shotgun, but I think the eye relief would work. I'll have to try it out at close eye relief to see how target acquisition is. There's a knack to getting good target acquisition with this 1" Ultradot with a handgun. He's familiar with scopes, so the best thing to do is probably to cave in and get the low-power scope.
By the way, in calculating the recoil I find that my son is about to learn how to deal with real recoil. His 20 gauge pump with a 3/4 ounce slug has more recoil than a .270 bolt action rifle.