There is a pick up alignment test in April scootering that might help identify a possible problem electrical problem.
One way of ruling out the choke sticking is by fitting a flip choke system to test it, this may not cure the problem but it's something you can tick off the list.
have you strobe checked the timing. I had a warm starting problem due to incorrect timing. The static timing by timing Mark was 19deg, (BGM stator and AF flywheel) but when strobed it was down at 17 deg.