Replace low pressure fuel pump?

I suspect I need to replace the low-pressure fuel pump on our 97 SN, GT-40 351 EFI. I'd appreciate your advice before ordering a new pump though.

We went out for the first time this year on the weekend. The engine started fine and warmed up normally as we idled out of the no wake zone. Then it stumbled and died a minute or so after I opened the throttle. Subsequently it cranked normally, fired intermittently, but wouldn't start. Here's what I know after a few hours of messing around...

No fuel comes out of the line from the low-pressure pump to the FCC whether the line supplying the pump is from the tank or a short piece of fuel hose immersed in an external tank.

Should the low-pressure pump be able to prime itself?

The engine runs fine at idle for several minutes if I pull fuel through the low pressure side of the fuel circuit all the way back to the tank return line using DIM's Suck Up vacuum pump. Then it stumbles and dies again.

One other concern is that when pulling fuel through the low-pressure side I see air bubbles mixed with fuel coming back through the tank return line. Is this normal or could my problem be an air leak in the low-pressure fuel circuit, or a leak and bad pump?

I've changed the fuel filter. Last year I added Stabil to the tank and made sure it ran long enough to pull some through the fuel system before we put it in storage.

It's clear there's a lot of expertise on this forum and I appreciate your advice!

Thanks,
Steve