The early (08-11) 13hp Kawasaki drivetrains were plagued with troubles, recalls, etc - the rear (driven) clutches were misbalanced and would often strip out, often damaging the output shafts in the process. There was a temporary fix some fleet providers were using in the form of a bolt-on balancer, but that wasn't a real solution, most were just recalled and refitted with TEAM clutches or after 2012, the new-style Kawasaki clutches (which are still prone to early failure) ...
Another major drawback to the 13hp Kawasaki drivetrain is the use of plastic gears in the governor assembly - disabling the external governor components can cause the rear end to over-rev and literally shatter the gears, locking up the rear end and causing an expensive mess to clean up.
As to the swap, no can do, the drives are on opposite sides. As to the extra claimed HP, I wouldn't put much stake in it, the Kawi is a single-cylinder engine which has a tendency towards vibration as well as a fairly narrow powerband. The old Fuji/Robins (pre-mid-0
295 and 350cc twins are MUCH smoother and develop a nice even amount of useful power throughout the RPM range, and overall are a much more pleasant cart to drive. I *will* give a slight edge to the new suspensions if You are staying on roads, groomed trails, etc but they tend to bottom out and get squirrely if You are doing any *real* off-road driving or are carrying multiple (3+) passengers.
Having owned/built/serviced hundreds of carts in the 6 years I have been in the hobby/industry, I would personally trade 2 carts w the Kawi drivetrains for a good older TXT if it were for my OWN personal use. That of course is just my opinion based on my experiences, I have many customers who are perfectly happy with their TXT/RXV carts and the Kawi's, although when we get those in we always replace the factory clutches if they already haven't.
Also, SteelPenguin, if Your 2002 is getting weak or You want more power, talk to Carrie at CT Rebuilds, for around $600 they will rebuild your engine as well as upgrade it to their "375" performance package, that will get you a real, useable 14+hp - pop another $80 to upgrade your driven clutch to 28 degree, another $35 for a shorter belt, and You will be AMAZED at what that cart will do.