Years ago, I had a buddy the used to use a Ruger 44 mag. rifle . Most of our shots are going to e 100 yards in. Personally I did not care for the effectiveness of the rounds past about 50-75 yards. The 410 slug ... I have no experience.
I think maybe you might want to stay with the 20 ga. Probably the recoil will be a factor at the range, but you can sight it in ... then let your son shoot a few times .... and I would bet that the adrenalin kick-in and concentration on his part to make the shot would ward off the "recoil" when he pulls down on a deer. Maybe the next day he might be sore, but he drops one I suspect all he will be is elated !!
If you can use a rifled barrel on the 20, that would be my suggestion. Much more effective range.