I keep toying with the idea of doing one. I have a dead 08 and a shed full (literally) of 350s and 360s part saws.
The air filter is different but there is also an adaptor that it mounts on to the carb for the 08. I don't see why you couldn't just leave the TS set up on it, unless you really want the 08 filter which isn't up to much (just a wire mesh cylinder)
The oil pump, and oil tank are an integral part of the side housing. I'm not sure about the drive, I can't remember, but I think there is a pin or something similar in the end of the crank that drives it.
Clutch drum would obviously need changing. Both bar studs are usually on a TS350, but not always.
Exhaust is different, but I don't see why you'd need to change it.
Not sure if the handle is different or not?