I am presently going thru the same thrash with My '63 +4. Starts OK but runs out of fuel on the hill. Mechanical Pump with an electric pump on board just in case.
Installed a Fuel Pressure Gauge. 3.0 PSI. Should be between 1.5 and 3.5. So not a fuel problem. Will check ignition next.
Turns out it was a faulty condenser. I am using Points at the moment. Have had problems with Pertronix. Now it is looking like Pertronix is better than points. What to do? So on my +4 I will carry a spare Dizzy with Pertronix in it. Pretty soon I will need a trailer to carry spare parts for this thing. Old Morgans are neat, but a PITA!!!!!!!!!