When you choke the ignition do you get any surge in power?
Primer bulb should be solid, no worries there.
Possibly a rebuild of the fuel pump is in order too. That's pretty quick and cheap to do.
Where the carbs get fuel, do you have an intake manifold? My last owner had like 3 tees installed, took me forever to figure it out because I didn't know it was supposed to have a proper manifold.
I do agree it does sound like a fuel issue, but I'm no expert.