To my knowledge there are no "crossover" parts. The reason briggs are cheaper is simple. They sell more parts. The KT series I parts are going up because the motor didn't stand the test. Kohler rebuilt it with oil pressure lube, and those engines were 5X the motor the original was. Look for after-market parts. OEM Kohler is out of line on their price. Here is a link to a site that has rebuild kits for what I would say is a decent price.
Kohler Rebuilt Kit KT17 Point is, search. It doesn't take too long. Google it, e-bay it, the parts are out there for better prices.
