My son has 2 of the 12 volt John Deer Gator riding toys. They are made by Peg Perego. The stock motors are some kind of a 550 I believe. It goes really fast on 24 volts but the motors don't last long.
I think a 775 brushed motor would do well in there. The motor mount holes would need to be enlarged to 1 1/8. I also eliminated the "shifter" that changes between reverse, 1st., and 2nd. gear.