You've checked all the stuff Chuck mentioned and some more...but, bear with me here, it's probably the gas + the Stabil. Granted IT should be fine...but most times this mixture along with sitting all winter stills make gummy stuff in the carbs.
Granted it may NOT show up at low speeds, light loads. BUT it MAY/WILL show up as you open the throttle more, much more for a full bore speed run. Then closing the throttle also adds to this... backfires, etc.
My 1st tank the bike does NOT run like it did when I let it set for a month, two or three. I try to drive some gas out, add fresh, drive some more, add more gas and then try to make some full rpm gear runs in 2nd/3rd gear to get onto the main jet. Sometimes it stumbles, bumbles and backfires but not all that bad. To me it's cleaning itself out with "new/fresh gas" and it takes about 50-100 miles till it's running just as good as last summer.
Having only a 3-4 gallon gas tank allows this "new gas" to get stale/gum-up very quickly compared to gasoline from many years past. All my bikes do this type of beginning of the riding season things. If my bikes DON'T clear up and start running like normal (within 2 tanks)...then I know I have more than just gummy slides, gummy idle jets, etc. It's the nature of the beast in the spring even with all the Stabil, fresh gas, engine fogging or whatever one does to store the bike for the winter months.