There are several possible reasons for excessive oil consumption in these older 'K' engines, so I'm not sure if you have covered all of them off yet?.
Use of correct Oil. It is often experienced that use of modern synthetic blends etc in these engines can cause high consumption. They were designed for Mineral based Oils.
A good 30 wt oil of spec as specified in the manual for air cooled, splash lubrication will always serve well.
It is also possible that fitting new rings to a worn/used bore will not improve it's current condition very much. It may be worn 'out of round' , of which there is a limit quoted.
As mentioned, deglazing a cylinder can work wonders for a tired engine, but it needs to be done correctly to resemble the finish of a newly honed engine.
Kohler recommend the honing marks should intersect at approx 30degrees, and if these marks are either too steep or shallow, the oil consumption/friction can increase.
Here is an example of the correct honing finish (after a rebore)-
There is another area to check, if not already done so.
The valve guides are a possible cause and can have the same affect as worn rings on Oil use and by causing the crankcase to be pressurised, instead of running
with a partial vacuum.
These are good engines and are readily able to be rebuilt, so I for one am pleased with your clear determination to get this one back up to spec.
I hope your potential engine rebore service is local to you.
It's a few years since I had a K301 fully worked by Sutton Rebore Services and I was so impressed by their standards and prices.
The sound of an almost 'back to new' engine running as it should is payment enough.
Regards