I have never seen your ped so I do not know what kind of carb you have so kust use what you can.
If you can take off the choke and idle very soon after starting from cold then you are running too rich. If not, the problem lies elswhere, weak spark or wrong plug maybe. I dont have much faith in the bad rings/compression theory, after all, the same stuff is above the piston as below it so who cares, if it has enough compression to run well.
If you are too rich, if your carb has an idle mixture adjustment screw, turn it toward lean. If your carb has a needle in the slide, lower it a notch, even though it is not supposed to affect idle. If your carb uses an enrichment device instead of a plate that restricts the intake, take it apart and check that the "rubber" tip is in good shape and the seat is clean. If all of this checks out, it sounds like too big an idle jet, is this replaceable in your carb?