Couple of more 'left field' thoughts:
When I first had my crossflow, I had big issues with idle jets blocking and (clearing themselves) which meant it would refuse to idle unless I had the choke out. It went back to Allon White but they couldn't fix it. In the end I fitted an uprated fuel filter, and carry a can of spray carb cleaner under the seat. It tends only to block about every 4 months or so now (rather than weekly) and a quick squirt sorts her out, I do about 8000 a year and have had her about 16mths.
Another thing might be the connection to the coil. I'm assuming it has a ballast resistor (if not, ignore this bit). As it would start and then immediately stop suggests that it was getting 12V from the starter solenoid feed, but losing power as soon as the starter is disengaged. Ballasts tend to run or not, but there my be something in the feed that is packing up when warm, then reconnecting when cool. The feed for the Ballast come from the back of the rev counter. It might be a dodgy connection there, or something up with the rev counter? I discovered this feed when I fitted my clock, and dislodged the wire out of the back of the rev counter!
