I might just bite the bullet and swap the engine. Then perhaps take it to a well-respected rebuilder who will do it RIGHT instead of putting a standard piston into a sleeve that's .010 over (I checked, it does indeed appear to have a sleeve installed) like the last rebuilder did.
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Here's the engine I have, its a Kohler K301 out of an unknown Cub, it was mounted in my parts 105. Not in horrible shape, and its complete and turns over. People it came from are a big Cub family, and the engine did run well before they parked it. I guess it didn't have anything wrong other than the absence of a carb, tank, and starter/generator. However, as you can clearly tell, while it was sitting it puked most of its oil out the rear seal and all over the back side of the engine, so I'll be needing a gasket and seal kit. Not sure how the oily mess managed to climb up the cooling fins either.
To swap it in I would install all the k241's shrouds, carb, air filter, gas tank and mounts, head studs (because this k301 has all bolts except for the one over the exhaust, probably because it's stuck in there), coil, condenser, Starter/generator, and basket pulley. New seals and some new gaskets, new head gasket, spark plug from the k241, perhaps the whole head from the k241 depending on the condition of the current one. From what I can see, it won't be very difficult to at least get this engine dropped in and functioning.
The k241, well, that's gonna be a bit of a challenge to say the least. I will definitely rebuild it or get it rebuilt, because I do want the tractor to retain the engine it came with.