BILL - If you've got a decent selection of hand tools, a K-series Kohler is easy to rebuild. The K-series engine manual & IH service manual are helpful, to the point of being required. You'll need an accurate inch-pound torque wrench, set of feeler gauges, a valve spring compressor and a piston ring compressor are handy to have too. And a harmonic balancer puller works good to pull the flywheel. You can buy or rent one from an auto parts store.
Most people rebore the cylinder and install an over-size piston, but sometimes you can get by with just a light honing and installing piston rings. There's instructions in the Kohler manual about how to measure the rod journal to see if it's out-of-round or tapered. The tolerance is pretty tight so most times the crank has to be reground. You'll need a micrometer to accuratedly measure the journal, something with resolution down to .0005 inches or finer. Most engine machine shops will measure this for you along with the cylinder bore. If your engine hasn't been rebuilt before the crank may not need to be ground, but I'd replace the conn rod anyhow.
Last engine parts I bought was about 6-7 yrs ago, things have gone up in price a lot since then, but if you use all OEM Kohler parts they should cost about $350-$400, piston comes with rings & wrist pin/keepers. New gasket & seal kit, new conn rod, new exh valve.
I've never replaced the governor gear in any Kohler, and only once had to replace the governor shaft because the machine shop broke the lever off of it.
Machine work, boring/honing the cylinder, grinding the valve seats, possibly grinding the rod throw, and planing the head for flatness should cost about $150 to $200. I'm allowing a little extra, things cost more out east.
With the rebuild, most people rebuild the carburator, install new spark plug, points & condenser, and points push rod. You should also read Dave Kirk's "KILLER KOHLER" write-up's, think they're still on the Puller & Hot-Rod forum home page.
It's pretty neat to fire up the engine the first time that only hours before was in pieces on your work bench.