some easy fuel delivery tests.
1. disconnect the fuel line at the carburetor, and direct the line to a container. have a helper crank the engine for 10 seconds or so, and observe the amount of fuel that comes out, and if there is any debris and junk in the fluid. did the stream of fuel flow in squirts, like a heartbeat squirts blood out of a carotid artery in a violent movie. how much fuel dispensed with 10 seconds of cranking? 8 ounces or so?
2. with the AVS carburetor (for example) the fuel fills float bowls. if the engine is dying because of fuel starvation, once it dies, carefully remove the top cover from the carburetor base, and observe how much fuel is in the float bowls. they should be about half-full. but are they dry or really low, like 1/8 to 1/4 inch full.
3. again on the AVS carburetor, with the engine off, when you manually operate the throttle, does fuel squirt out the accelerator pump tubes onto the barrels? is it a nice decent stream?
4. when you "rebuilt" and cleaned the carburetor, did you find obvious junk within it and/or stuff at the bottom of the float bowls.
5. there is screen on the pickup tube inside the fuel tank. if there is a bunch of rust and debris inside the tank, (it would take 8 ounces of debris or more) if could be plugging up the pickup. while it's possible the screen has worn out or torn, chances are, it has not, and the fuel lines are clear. you would have to drain the majority of fuel to remove the sending unit to inspect the screen to see if there is junk caked onto it.
6. prior to the carburetor rebuild, when the engine died, did it die immediately after releasing the key? if so, you may have an electrical, ignition, or ballast resistor issue. how is the health of the spark while cranking? and the cleanliness of the cap and rotor area? points ignition, battery voltage, etc? do the spark plugs look healthy?