I'd check the cleanliness of that carb again #1
The choke on these carbs is supposed to stay locked open or closed, so something is not right there.
Also the screw is for very fine tuning, it will not make enough of a difference in how it runs for what you are explaining.
You'll need to pull the carb, and take the jets out. Check what sizes you are running, because its the jets and needle that do 95% of the work, with that screw only doing the remaining 5%
Learn which jet is which in the carb and remember as follows.
Pilot jet impacts throttle: closed - 1/4
Needle impacts: 1/4 - 3/4
Main Jet: 3/4 - Full
You need to play with the jetting and get the engine to run smooth. Start off with the pilot jet. Get it to idle and run smooth. Once it is idling smooth to the first 1/4 throttle you are in a good ballpark with the idle. Remember at this time to leave the adjustment screw at the standard start point (i believe at 1.5 turns out)
Next you want to focus on the main jet. Make sure that the engine at full throttle runs smooth.
Finally you Adjust the needle and its clip position. You want the engine to run smooth with no popping/backfiring/spuddering (lean condition) or bog (rich condition). Finally when thats all done you smooth out any small discrepancies with the screw (this is where that final 5% comes in). When this is all done you should be good to go. Dont forget to also check your plug and make sure the color reads good.