I had it in mind that you would replace the rings yourself. IIRC it was part of your plan at the beginning of this project, to learn how to do normal repair operations. You could not hone the cylinder yourself, but that is a ten minute job for the average mechanic, if it needs to be done.
So far as the old carburetor is concerned, I think you need to keep it both for spare parts, and for practising on.
I'm not sure it's necessary to remove the engine just to replace rings. It is a matter of removing the air cowl, removing the carburetor and muffler, then unbolting the cylinder head and inspecting the cylinder bore. Then if you are going to proceed to replace the rings, you'd unbolt the base of the cylinder, and slide it off the piston. You should be able to tell from looking closely at the under-hood area on your mower whether you have room to do this without taking the engine out. If the bore and piston look OK you need to remove the three piston rings from their grooves and replace them with new ones, and put everything back together. You would need to scrape the surfaces of the head and top of cylinder, and you would need a piston ring compressor to put the cylinder back on over the piston. You would need a new head gasket. If you don't need to take the engine out, the whole procedure would take Joe Carroll less than 90 minutes I think - maybe a lot less. I'm out of practice, I'd take longer. It isn't like playing a harp in an orchestra, it's pretty basic stuff.
