It seems counterintuitive, but lean it out until rpms increase, then lower throttle setting and lean it some more. If it stalls, back it out. If you can't dial it in, it could be a carb blockage like you suggest. Rigorous cleaning requires disassembly and soaking, then spraying with carb cleaner and maybe compressed air. If you did not remove the domed plug up at the top, you should do that and clean the idle passages under there -- need a kit for the replacement expansion plug, although I've patched and reused them using epoxy.
And it's possible you are not getting a "lean sneeze", but running rich (stumbling). If backfiring through the carb, there might be a problem with the reeds, but not very common.
[ed. With poss. exception of the h.s. orifice, can use soft wire to clean all openings -- that and spray cleaner.]