No Gas to the Carb When Engine Warms Up

I wouldn't recommend doing that, You could easily blow the screen off the pick-up if You're not careful, and pressurizing the tank won't tell You anything related to the stalling.
The gasket for the sender can leak all day long, the only thing it will do is kill Your MPG & stink up the garage, it has no bearing on fuel supply.
Given the cap-off reply, If You can get it to run dry/near dry, I'd try removing it and observe what results that produces w/a helper,(& maybe a portable jump pack).
If the sending unit gasket leaks, won't that suck air when the fuel pump is pulling fuel? I was going to blow out the lines after I disconnect the fuel pump. After I check everything out, I may pull the tank and check the fuel line above the tank, it may be kinked from when they replaced the truck floor.