Okay,... I'm thinking your choke/enrichment valve isn't working ....
Pulling it out all the way, should bump up your idle speed quite a bit... if you are having to crank the idle screw as well, the choke isn't doing it's job...
Carb cleaning with special attention to the enrichment circuit...
... a little variation in the idle speed as engine heats up is normal, but it should rarely require adjustment, if at all...
I doubt that I'm telling you anything that you didn't already suspect...
... just dreading having to go through the carb again, huh?...
...
Best of luck...
You might check the enrichment circuit diaphragm on the opposite side to the choke,... but if that puppie's leaking, it's a $45.00 part...
I think it's only supposed to work on decel, but if it's leaking, I don't know what happens...
http://www.ronayers.com/Search/N/687/PartNumber/13480-05A10/Source/SU