re: "1 - I know you said the carb was well cleaned, but did you remove the screw near the top of the carb and clean the passage under it? It is the idle passage."
Been there, done that ...believe "hondadude"! No amount of "cleaner" and or "blowing" seems to clean this passage once it gets crud in it.
To clean this passage I used a single strand of copper wire that I peeled out of the twisted wire in a length of lamp cord. A magnifying glass (my eyes aren't a sharp as they used to be) and a pair of tweezers to hold the wire complete the "tool kit". While this is doable while the carb is on the engine, I prefer removing the carb, removing the main jet ( the one that is in the end of the "snout" that sucks up the gas out of the bowl.)
A few strokes with the wire and a couple of taps of the main jet end on a paper towel) worked just fine for me. I was satisfied to actually see the piece of $h1t that clogged my idle jet. A couple of blasts of air from an "air can", into the top of the idle jet passage completed the fix.