If your fuel tank pick up tube’s bottom screen is plugged up, it will require a through tank cleaning, not just a shot of air (and agree bad idea).
With your dual engine set up you have the best troubleshooting arrangement possible. Start at the Fuel Pump side and swap the hoses even if need to add a short extension. If the problem moves from one engine to the other, then it’s clearly upstream of the fuel pump (hose, anti-siphon value, plugged pickup tube, etc.).
If the issue does not move, then it is the fuel pump or something downstream of it.
Oh, it also occurred to me that a fuel pump not being able to continuously draw fuel could be a loose or blocked fuel filter. Loose and it sucks air. Blocked and it does not allow it to pass.
Let us know how it goes.