I think you are on the right track trying a temporary gravity feed system, air bubbles feeding the carb is not good. If it idles and runs fine with the temporary gravity feed system, then your problem is the fuel pump. If that doesn’t solve the problem, check out your carb, make sure fuel flows when the floats drop and fuel stops when floats rise. Also check fuel filter for being clogged. Lack of fuel in the bowl is a concern, that should not be happening, sounds like fuel is not getting to the carb.
Hope this helps,