Here is the
post that Mike shared related to his pickup coil heating up. When it got hot, the bike quit. Cooled down and started. He checked his pickup coil with an old style voltmeter which gave a pulse when a magnet was waved over the coil. I think our flywheels have 2 magnets situated in the appropriate location to give the 270 degree firing pattern. This info might help track down the problem which has me stumped given the fact you switched and replaced pretty well everything.
One other item, I just checked the part number for the pickup coil for the 360 and 270 engines and they are the same telling me that there probably isn't two separate circuits. There are two separate magnets though in the flywheel. Is one of your magnets missing??? Could it have fallen out?
If you changed the CDI unit, coils and the pickup coil/magnets are good then the only other thing I can think of is the harness from the pin-out of the CDI unit to the coil shown in the print. Good luck.