The tranny in the craftsman is a tecumseh/peerless MST200 was as the other mower is a mtd yard machine type more with a mtd type gear transmission and are not interchangable. You might be able to find another mower with a hydrogear transmission that will bolt up. Peerless is now owned by Husqvarna. The problem with the tranny may be something as simply as needed to be bleed. Jack up the rearend and let the wheels spin and see if it improves. Also check to make sure the belt isn't bottoming out in the engine pulley causing it to slip.