Let's forget about your carburetor for a minute. Something else (I believe is causing this) although you do seem to have some carburetor (and fuel pump) issues. We can certainly address those later. But for now...
Exhaust system blocked anywhere? This will cause this to happen.
Bad ignition coil. A broken down coil will cause this.
Dirty air filter. Same as exhaust blockage, really but working on the other side of the breathing affair.
Compression loss? You said the engine was rebuilt. I've seen things (unexpected things) go wrong right off the bat, so we can't rule it out.
Bad spark plugs?
Toasted vacuum advance biscuit?
Other ignition problems?
