Like the Fonz, I run a 15x5x6
Carlisle X-Trac in the rear and a matching size Carlisle Snow Hog in the front (for turning, as mentioned). The X-Trac will wheelie me in 6" of mud if I hammer it about mid-way through. Of course I'm running a TAV-2 and a 250cc briggs motor. But the tires are amazing in the dirt, mud, and on hills. They are directional, but we run them backwards for more grip. You should be able to ask your local small engine repair shops, since they are just snow blower tires.
With the Baja Mini, you will have more ATV tire options since its a bigger rim.
My friend with a Mini is running the jackshaft setup that came on it and it is really quite capable. Where it dies is in mud and slick stuff. It is just a geared down centrifugal clutch in there, so it needs to be turning a pretty decent RPM to hook up. He would have to push it when he spun out in the mud and on a couple hills this last weekend. Depends on the sort of terrain that your running it in as to how it would work for you. Should bolt up fine, but I imagine you would have to modify the frame like you would if you were installing a TAV on the DB. Never done it though, so I can't say for sure.
If you want your son to be able to climb hills, and money were no object, I would get him a TAV-2 and the optional governor. Its really just an adjustable ring that clamps around the drive inside the TAV and keeps it from opening up all the way, whereby reducing the top speed. They say down to around 12-15 mph on up, depending on where you set it.