DoOver,
If your Kohler is running, and you want to stick with a Kohler, I would opt to rebuild yours. The "pulling" guys have a-lot of tricks to get some extra hp out of your stock Kohler, and if you found a guy to do a rebuild, that is where I would head.
The 1000 series was available with 14 and 16hp engines, but, if I remember right, the 1450 and 1650 had slight frame modifications to allow for the bigger engines. I believe the 1650 had a section cut out of the frame to allow space for the larger flywheel, but don't quote me.
Honestly, I think I would stick with the same 12-hp and a rebuild. You could re-build it a couple of times for the price of a new one. Now, if the connecting rod or crank broke, or the engine is siezed, throw it away. I have never seen a rebuilt Kohler, where one of these things has happened, that lasted more than 100 hours. I have seen a few even that lasted for only 1 lawn mowing, and then blew up again. IF you go for a rebuild, go to someone who REALLY knows Kohlers.
As for motor mounts. I have mixed feelings about the solid mounts, but many guys swear by them, and those guys may have a-lot more experience with them than I do. My uncle had a 1000 that I must have put 3 clutches in, then finally upgraded the ISO mounts to the new replacement ISO mounts, and that clutsh is still running after 6 years. He mows about 3 acres with it.
That mower on e-bay is not all there, missing the casters and guage wheels, I would guess that it should not go for more than $150 or $200. Mine was complete, in very good condition, with no rust, and I got $500 for it. If you grab that one on e-bay, be prepared to spend some $$ to get the missing parts. They are big, heavy duty casters and such, and probably will run you another $100, if I had to guess.