Ok the fact the angle of lean of the bike when not moving affects the idle def leads me in a new direction,
So, it sounds like some kind of feul level , float height thing?
Also you cleaned and synced but did you check and replace the worn parts? Maybe a worn float needle thingy, the one with the plastic tip that the float pushes up to block fuel flow into the bowl. The plastic tips wear out and if you didnt remove the floats u mighta missed...
Only other idea i had is maybe you have a vaccuum leak, that when the bike is tilted somehow seals up, and when u straighten the bike, something moves and the leak occurs?
These r not answers.still, Hope they can aid you in some way.