I have a mower with a Craftsman 15.5 hp Kohler engine (917-256552). I'm getting lots of gas in my oil. Cause? Coulod I replace the Kohler with a 16 hp Briggs and Stratton from another Sears mower (917-270670)?

Yes you could but you would have to replace the wiring harness also.
But it sounds like you have dirt in the carb, keeping the float from closing and allowing fuel into the engine block through the valve guides needs a good carb cleaning.
Luck

I am with DG on this. I have had a few Kohloers do the same thing, my pressure washer is doing it right now. Good carb cleaning and maybe just swap out the needle