The engine has carburetor mounted on top of the fuel tank. Either the tank mounting gasket is leaking, or the diaphragm for the fule pump section of the carburetor is defective, have you rebuilt the carburetor with new diaphragm? See basic link below.
Fuel pickup was used from old carb, or did it come with the new tube and screen?
Same problem with old carb?
No, it might not show as a fuel leak. Tank has to seal.
I could be and you would have to straighten the tank mounting with a file, or add an extra gasket to let it seal better. Something else that could affect the fuel being drawn into the cylinder is the valves. You may have intake valve that has no clearance or is leaking, not building vacuum in the cylinder to draw in the gas charge.
Fuel tank cap would only affect the running, not the start.
Use the link in your email to get back to here. You can check the valve clearance through the vent cover, without removing the head and valves.
This is the flat head engine with the valves in the block. I wonder if the valves may be too tight and the engine does not have enough vacuum to pull the fuel charge through the carb , to the cylinder. Have you ever checked the valves or the compression?
OK> Let me know.