Crazy idea

With a completely empty fuel system, I fill the tank at least 1/4 of the way, use a MightyVac to pull gas up to the fuel pump (or blow a bit of air in the fuel tank), and fill the carb float bowl(s). Assuming you have a good fuel pump, it will start and run just fine without it dying on you.
Yea that is pretty much exactly what my idea is! Just use a cheap fuel pump to prime the lines and carb.