I don't like the "little putt" Mark, something is wrong. OHV Hondas do not miss shots. If the throttle was oscillating I suppose it could happen, but otherwise, it could be a leaky valve, blocked muffler, or something else nasty.
I find those engines (GXV120, 140, and I suppose 160 though I haven't worked on one) very pleasant to work on. It is like an American car from the 1950s, before they got complicated. Everything properly bolted together, proper piston rings, and an air of lasting forever provided you replaced a few wearing parts at very long intervals. Of course in those days there was lead in the petrol, so you had to service spark plugs and replace mufflers and exhaust pipes all the time, and now you have gum in the petrol so you have to service carburetors all the time (meaning every few years), but it's a similar kind of thing. Working on Hondas is a civilised way to spend your time, without all the cursing, damaged parts, and trying to get a few more years out of bent-tin adjustments.
