OK, so you are saying that the fuel tank is clean and rust free on the bottom, correct? And, you have pulled the intake, and the check valves are OK. You also say that the engine runs OK until the carb runs out of fuel. If this is the case, you should be able to keep the engine running by pumping the primer button continually while the engine is running, have you tried this? I think you said you have, but let us know. Are you running the engine in a tank, or on a boat?
I know this has nothing to do with fuel delivery, but have you had a look at the coils? This is easily done by simply removing the little inspection cover off the flywheel and looking inside while rotating the flywheel. You are in trouble if the coils are cracked/split.
