Truck seems starved for fuelbut will run until it's put in gear. Details below.

Check the fuel pressure,you are right about the pump i think,when you put in gear it need,s more fuel and can,t get it,again check the fuel pressure and it will let you know it is the pump or not.

Check your spark plugs/wires & coils & TCC. Clean throttle body & IAC with throttle body cleaner and install with new gaskets, clean MAF with MAF cleaner(do not touch filament). Check for vacuum leaks, the 90 degree small vacuum connections under upper intake crack open easy, replace with the new style from Ford Service parts department(1 at back and 1 toward front center). Clean PCV and make sure its in the valve cover good. Mine is a 98 and last year did exact same thing stalled everytime I put in gear until I did above. 2 bad plugs, both vacuum boots cracked, pcv hanging out the valve cover, throttle body and IAC dirty. All combined, seem to do it all at once but takes time. You can test the plugs look online for procedures, best to change the wire set out if 5 years old or more and use dielectric grease on boot connections and keep them from crossing each other. Make sure wire boots are tight on the coil packs terminals post.