When you checked the contacts in the shop, they just happened to be working at that time! Monitoring the coil voltage is the thing to do here.
Also, is there a speed associated with this problem? If it works fine (when it works) at higher speeds, then it's probably not a fuel problem.
Another thing to realize, the carb may be prone to vapor lock if it is not properly heat shielded. I don't know if this is the case with you, but it is something to keep in mind since you indicate that the problem is more frequent when hot.
On their death bed, nobody ever said, "Gee I wish I'd spent more time at work!"
'68 Sprite 1275
'76 Midget 1500