Rings don't sound too bad, and cylinder wear is likely not bad either, since the end gap only appears tonchange .002" (as per your notes) going down the bore. Since diameter is 2piR (or piD), that makes diameter variance less than 1/1000" top to bottom, and assuming that your lowest measurement was at the absolute, unworn bottom of the cylinder, then my 'scientific back-in' to wear should hold. Note in the manual ****, it says that service specs for rings are more like 1mm, which you are nowhere near. Neither was my GXV140, but it smoked like mad . . . and a re-ring too it to perfect.
For a home, I did as you did and got the loaner from the car parts store. The goal isn't to remove metal, but to just take the glaze off the bore so the new rings will seat.
Oh, and most Honda parts sites will take you to the specific engine and rings based on model and serial of the mower itself . . .
And even if within wear spec, I see no reason not to replace the rings, since you are that far in already. Not sure if the GCV has valve seals, but iff it does (or one was added in later production, as in the GXV) then I suggest you look into it. You might want to refresh the upper and lower crank seals as well while you are there - they are pretty cheap, and a pain to have to go back for. (On mine, due to age, the seals were basically falling out of the case . . . made a huge mess, and one of the main reasons I went into = m]it).
Basically, if an older engine, and I'm in it, I tend to replace any seal subject to wear or deteriorization.
- Tim