The shut-off valves are pretty inexpensive, it may be worth trying. Can you swap with another machine? Maybe it is a fuel line, or a clamp or connection to the valve. I had a leaky fuel line inside the fuel tank on a Gravely recently, and it wouldn't pull gas up. Very cheap repair.
Does it have 2 fuel tanks? Does it happen on both fuel tanks? If so it is probably "after" the petcock.