Single line petcocks have been reported to feed plenty of fuel. It's only a single port (and then the reserve port, which is usually closed) from the tank to the two taps. The port is smaller than either tap. Installing a single line petcock just makes the T visible. It also does make a bit more spaghetti, but it certainly works.
I should have a spare tap somewhere with a good screen, but as I recall they are press fit plastic pieces... and probably quite brittle after years of sitting in gasoline. Probably better off putting good guts in a tap with a good screen.
You could also try soldering a fine brass mesh over the torn section of screen. I resoldered part of my oil screen because it was separating at the seam, but there was also no plastic there. If you have the old style tap with the straight pipe and a small screen at the top, you might also be able to fit a brass filter element over the top of it.
Filters are nice, but a steel tank will drop rust which eats away at the seals in the tap. If you want to do away with the screen, consider coating the inside of the tank.
If it ain't broke... well I'm sure I can find something that is