I thinking the change in food upset his digestion. That part is normal and common (any change in diet). And to an extent kittens have softer poop. Should clear up quickly, but get him back on the purchased formula. If the diarrhea doesn't stop, a vet visit is in order.
You can then start transitioning him to solid food. Mix solid food into the formula and encourage him to lap at it. Gradually make it more and more solid. Just like you are doing.
Sounds like you can stop the stimulation. He's got it handled now. But watch, just in case.
I've never had to teach a kitten to use the litter box, just put one in the kitten area with a little litter in it. At first they will play in it, getting litter everywhere, then they'll start using it and continue playing in it.
Imp