THe petcock is the next thing to check. You'll have to drain the tank of course, but the petcock assembly is pretty simple to get apart, clean up and put back on.
Before you take it apart though: disconnect your fuel line, and watch gas run out the petcock on standard and reserve. It should 'run' not dribble, and it should continue to run any length of time. It it does this, then maybe the problem is in the carbs (there are filters there too).