[Modelacoupe3]

I experienced a similiar problem on my 30 coupe. It was the wire between the upper and lower distributor plate. The wire connector to the upper plate was installed incorrectly. The wire connector was so close to the metal surface on the upper plate that it would ground only after the the engine would heat the distributor. Also make sure this wire is the correct one, over the years they were replaced with the wrong type of wire. The incorrect type of wire will break over time with the movement of the upper plate while retarding the timing to start the car. Brattons sells the correct multi strand wire.
Another option would be to borrow a friends distributor for diagnostic purposes. If it solves your problem you have narrowed down the problem. The same goes for the carburator. It is always a good idea if you do much touring to have extra units (rebuilt and tested on your vehicle) on board.
Hope this helps you solve your problem.

Scott