It would be a great home project to rebuild your motor if you had the time and tools and skills. Otherwise, if the rest of the unit is in good condition, it's only a money choice, if you don't count your own labor. $300+ is still money saved.

This is one of the most dreaded situations to be in.
Engines that have seized due to lack of lubrication are difficult to rehabilitate, there are just too many "what ifs" to make all the failures fit a repair pattern.
Or, in other words, each engine failure (due to low oil seizure) can have different and varying damage to a number of components. The more components damaged, the more expensive the rehab will be.
Determining whether a seized engine can even be repaired is not a task for a novice! The inexprienced, untrained eye can fail to recognize some types of damage and the engine may suffer immediate "failure" when returned to service, and all the efforts would have been useless, and now, even more expensive.
I will suggest you visit the Kohler Engines website and download a free copy of the service manual for this engine.
Study chapters 9, 10, and 11 very carefully (and repeatedly). If, after studying those chapers, you feel confident that you would be able to handle a teardown and inspection.........then, you can take the engine apart to see just how bad, and how extensive, the damage is (expect total destruction but hope for a miracle).
You need to use a digital camera to document your disassembly, take lots of pics as you remove parts, draw sketches, make labels, bag parts and fasteners in groupings.
And more about those pictures.......post pictures of the damages once you get to the point of seeing what part(s) seized. If we can see the damages with our eyes, we can advise you whether it is wise, or unwise, to continue.
As I said in my opening, this is not a good situation to be in.

If you blew up the engine due to lack of oil, the crankshaft, block, piston, and rods could all be unusable. Why not replace the short block and reuse your cylinder head, carburetor, ignition, etc.

Replacement shortblock #1252251 is between $600 and $700 on the Web vs. $1000 to $1100 for complete engine.

Thanks for the input..I am dismantling the engine now and will post photos to assess damage. I think a short block will be the best route.

I don't know, I went with the complete motor instead of the short block on my Tecumseh retrofit. $300 is not a lot for piece of mind and no hassle install between the short block and long block, especially if the long block/complete motor includes a new carb. You have to make sure you torque all the head bolts correctly and the head gasket seals up around pushrod tunnels, maybe a re-torque is advised after a short period of running. And then the question, did you damage the rockers and rocker shaft when it ran dry? Nobody's going to take back the short block for that, but they will the complete motor.

The problem with Kohlers is that if a connecting rod breaks, it usually trashes the camshaft, and takes a chunk out of the bottom of the cylinder bore. I've found crankcases and components up on eBay motors for short money, not a bad route to take, and they are very simple, straight forward engines. Crankshafts I re-use, even if there is metal transfer, which cleans up nicely with muriatic acid.

Kohler told us that their engines can use up to two ounces of oil per hour, which is why this is a check daily item.