I’m just gonna throw this out there......

Maybe you already mentioned it....... but have you tried a Holley carb on it?

Possibly a friend has a known good working one you can just stick on and try.

Sounds like you’d be able to tell pretty quickly if it offered any improvement or not.

In my mind, if you tried the “hose in the gas can” thing where you bypassed the rest of the cars fuel line, and the fuel pressure on the gauge was still jumping all around, that sure sounds like a fuel pump problem to me.
“New” doesn’t necessarily mean “good”.
I don’t see how the gauge could jump back and forth from 7psi back down to 2psi unless the check valve in the pump is faulty/stick/leaking.
If the pump you have is of the “high performance” variety, some of those have 6 valves....... and any one of them could be leaking.

I assume you’ve pulled the top off the carb and verified the float height and float drop are correct.