Summary of below:
re-installing old rings (that have been run in and seated especially) if they have been removed from the piston is most generally not a good thing.
I only seen page one before I typed this below. did not see pg 2 & 3 My fault
Just curious.
It being a one cylinder:
Was the cost of new replacement rings to pricy?
or were you not sure of the correct part number for replacement rings? (due to only guessing at a model number due to no air cowling info)
Just some things I've noticed about comparing old rings to new rings on small engines
I've taken a new ring ring and could actually see the difference in the expanded strength as compared to a old ring. Old ring/rings looked ok when a new replacement ring was not available for comparison. (lay the new ring on top of the old ring and the new ring has more expansion strength out of the cylinder which indicates stronger scraping force against the sides of the cylinder) The old ring/rings have less expansion force against the sides of the cylinder.
The old ring and new ring end gap was same when in the cylinder. (but also if the end gap of the new ring is quite a bit less when in the cylinder (Using the piston to push the ring down square into the cylinder) so as the end gaps of the new and old can be gauged for comparison) can indicate that the old rings edges are worn.
You say it was not smoking before the tear down inspection. It might wear in and slow down on the smoke as indicated but I think if the cylinder is not tapered and the intake valve stem clearance is within specs a set of new rings would probably reduce the smoke.
But as indicated due to cost of set of rings for 2 pistons (Briggs for example) at $100 or more and other parts/seals and gaskets just for a two cylinder can be too cost prohibitive with labor involved and I only do small engine overhauls for myself now days.
Trying to judge the condition of the bottom oil control rings was always ???? for me.
I could not, for the life of me, figure out just what changed that would cause this. Also, I did not install new rings when it was apart because the bore and ring wear was relatively little, plus the fact that it is my understanding that if you are installing new rings (regardless of bore wear) that is mandatory to hone the cylinder. I believe that my surprise and disappointed that it (now) smoke is a reasonable and valid reaction, no? 