Weak fuel pump?

Red, since you are having such a fight, I think it's time "to get serious."

I assume you have ONLY a mechanical pump?"

Put your pressure/ vacuum gauge back at the rear and crank the engine. It should pull at least 12" vacuum

Now unhook the line to the carb and devise a way of plugging it quickly. The best you might be able to do is a bolt with a smooth unthreaded section, and a clamp.

Again crank the engine, develop vacuum on the gauge, and as quickly as you can, plug the front carb line and clamp it.

Now watch the gauge for leakdown.

This business of the "empty filter" may be a red herring. The fuel may be trying to boil, and as the needle opens, the fuel suddenly expands and vaporizes, until the pump keeps up. I've seen lots of cars that ran perfect with a partly or completely empty filter, although if you run it a couple of minutes you can see fuel "coming and going."

Even though you replaced the pump, have you run a capacity check? You may have a problem with the eccentric.

And don't forget--"new" does not mean "good." The new pump might have a problem. OR if it got a little dirt into it, the pump valves may not be working