Sure you can. However, it may not be quite as easy as you're imagining. You'll have to re-plumb the supply and returns lines, move them from the FSV to the tank of your choice. And you'll have to re-do some wiring if you want the fuel gauge to work. All those things run through the FSV as Ford built them.
You just installed a new lift pump? Are you sure you got the arm under the crank rather than riding on top? Honestly, though, your problem sounds like the classic air intrusion. They can be a ***** to find. I'd start by replacing two return lines with clear lines, fill the fuel filter, and let it idle for quite a while, all the time watching for air bubbles in the return lines. If no bubbles, hold the throttle open some and watch more.
Try disconnecting the supply line where it enters the fuel filter. Crank the engine for ~10 seconds, see whether you get fuel out the end of the open line.
What you're trying to do here is isolate any possible air intrusion.
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