Hey Andre I wouldn't worry to much about the petcock. You said you removed the tank with it in the off position and no fuel flowed out. But like you say even if you leave it on the needles shouldn't allow any fuel to drain in to the engine. Just for reference my petcock is in the on position right now just like it always is and I've never had a problem.

A stuck needle will usually overflow out the carbs overflow tubes. A worn seat or needle will do what your describing. Replace the seat and needle just to eliminate that issue. They aren't that expensive and fresh carb parts are always a good thing.