Cleaning or replacing the tank sounds like the real solution.
You're thinking of a little tube of screen fit into the pipe nipple stuck in the bottom of the tank. Not much trouble to make, I've made them to replace similar screens on small engine fuel tank valves. Roll up a piece of suitable brass screen, slide it in the fitting and solder the seam as well as at the fitting. Your choice to leave it open or crimp and solder the end.
Or a few years later the fuel sending unit includes a pickup tube and on that is a screen "sock". You could swap and use that type sending unit / pickup.
