First things first.
Tee off at the carburetor inlet and run a copper line back to the firewall, then up past the hood lip and onto the grillework (cowl) between the hood and the windshield. Mount a mechanical, liquid-filled fuel pressure gauge on the cowl temporarily and read the fuel pressure gauge as you drive. You'll need a steady 5 psi of pressure in order to fill the carb without overpowering the needle and seat, so monitor the pressure through the windshield as you drive. If it's too low, replace the pump or look for restrictions in the line(s) from the tank. If it's too high (over 6 psi), regulate the pressure down to 5 psi with a regulator or replace the pump with one that will limit pressure. Once you get the pressure under control, you can begin to test for other problems in the system.