If no gas is leaking past the shut-off valve when it is shut off indicates the entire issue is in the carb itself. The biggest single issue could be the float valve being set too high. That is critical. But there could be issues with several other things. Tom Endy has a couple articles on carbs at his site that are probably something you should take a look at.
Go here and page down to Fuel:
https://www.santaanitaas.org/tom-endys-tech-articles/