The fuel selector is a fairly simple device. Leaks can occur when the 4 hole gasket hardens. But, the drip you have is probably the two fiber washers failing (or missing) on the two screws that hold the valve to the tank body.
As for fuel flow, test it!
Time how fast it fills a container and note the volume.
These bikes, at worst, get about 30 MPG at 60 MPH. At that speed it takes 30 min to travel 30 miles, using 1 gallon of fuel. 15 minutes would use 1/2 gallon, 7.5 minutes would use one quart. 3.6 minutes would use 1 pint. 1.8 minutes would need 1 cup of fuel.
So, time how fast the fuel comes out of the tap to fill one cup. If it takes less than 2 minutes, the fuel tap isn't the problem.
I still think you should replace the old filter. And, I still think you should look at spark plug deposits to determine lean or rich combustion conditions.
Also, when it quits, check the head pipe temps. Do all cylinders fail in unison? Or, do some stop before others? Ones that feel colder can help point to fuel issues at the carbs.
Still haven't checked the valve clearances, I suppose.