Typically, I would say that you should never be able to read suction on the fuel pump output line. So, sounds to me that there is a problem with the pump. I doubt the rubber diaphragm is at fault, those rubber diaphragms in the Airtex pumps will withstand an A-bomb explosion. It would almost have to be one of those check valves in the bottom of the inlet chamber.
There's another problem though, and that is her Holley 2110 (ECG) carb is leaking gas out of the float chamber dry after a couple days. If there was enough gas in the carb to start and run the engine for a few seconds, even a partially faulty fuel pump might be able to pump enough gas up to the carb to keep the engine running.
I am not saying you should fix the carb and forget about the faulty pump. The output pressure of a good new Airtex pump might be a little higher than OEM specifications, but it should not be enough to negate the carb float, which would flood the carb immediately. I am running a Ford EBU carb on a 292 Y-block with an Airtex pump and there has never been a problem.
Things to check on the carb: busted power valve (economizer) diaghragm will leak all the gas out of float chamber. Also test to see if the accelerator pump ball check valve is not seating properly in it's hole at the bottom of accelerator pump chamber.
The Holley 2110 ECG (1956) works exactly same as the Ford EBU (1954/55) and Holley 2100 (1955), except the 2110 has bigger throat and larger venturies than the previous years.