My first thought is to ask if the filter sock on the fuel sending unit was been changed. If the fuel filter at the carb was gunked up, certainly any such gunk would be clogging the sending unit filter sock, which is simply slipped onto the fuel pickup steel pipe inside the fuel tank. I know dropping the fuel tank is a real Pita, especially if it has 1/4 or more fuel in it. One quick trick in dealing with a clogged sock (do not do this with a full tank) is to remove the fuel filler cap, then at the sending unit steel fuel pipe outside the tank blow a quick shot of compresses air into the tank. I idea is to use the blast of air to push the filter sock off the pickup tube. Please note, I have not ever done this, and likely never will unless the fuel take is no more 1/4 full. If I suspected a clogged filter sock I would be inclined to drop the tank and remove the sending unit so I could do a proper inspection of the filer sock.
I would also want to test the fuel pump to make certain it is producing both the volume and pressure outputs. If either test fails the pump will need to be replaced. I would also, in the event of a fuel pump failure, I suggest sniffing the oil on the dipstick to see if it smells like gasoline is in the engine oil. The reason is when a fuel pump diaphragm fails it can result inan external and.orinternal leak. The internal leak can end up sending gasoline into the crankcase, which will contaminate the engine oil and compromise the oil's ability to properly protect the engine's internal lubrication.
If you have yet done so recently, I would also be replacing all the rubber fuel lines at the fuel sending unot and at the fuel pump's inlet (and at the fuel filter near the carb while you are at it). The reason for replacing the fuel sending unit and fuel pumo rubber fuel lines is because theya re often ignored over the years, and when they begin to harden and crack, they can introduce a leak where air is pulled into the fuel line instead of fuel being pulled forward by the suction caused by the fuel pump. Worse, they can leak liquid fuel (in addition to sucking air). For the fuel line at the carb fuel filter, it is a matter of not having an older rubber fuel line that begins to leak - right abouve or nrear the ignition distributor no less.
Clearly, there are other things that can cause the issue you are having, but I would start with the fuel system. Other things to consider are a possible failing ignition coil, a failed or failing ignition condenser, points thatare closing up that causes inadequate ignition point gap (or excessive dwell), an excessively worn distributor upper bushing or breaker plate that causes inconsistent ignition point opening. I have seen lots of other causes of issues like the one you are facing, even one case where a vented fuel cap was no longer venting, and the engine would fuel starve because of the vacuum pressure inside the fuel tank as the fuel level went down while the engine was running (the owner had gone to several shops before he came into our Ford dealership. I had it diagnosed within 15 minutes, lucky stroke).
I hope this helps. I look forward to future posts in this thread letting us know of your progress. And once you locate the problem and correct it I hope you will share that also.