Ok so I am working on a 01 exp with the 4.6 in it. It had a very bad miss,would hardly pull its self on flat ground. The truck has over 200,000 on it but motor was replaced 3yrs back with new one. CEL was on had CYL 5,6,7 miss. I pulled the coils and most of the boots had moisture on them and rusted springs. I cleaned the terminals installed new boot/springs and filled with electric grease. Tested all the coils with spark tester and all good hot blue spark. Now after reinstalling them the truck runs much better! The problem now is hard start, missing under load and shudders/bucks at 45-50mph. Im thinking FP, seams that when I first turn the key after sitting all night the pump hum is less pronounced than after I get it to start. Its only hard to start if it sits over night. If I turn the key on and off a few times the hum from the pump get louder and then it will start right up.When the truck is cold it runs perfect! I havent hooked a fuel pressure tester up as mine is busted and didnt get a chance to pick up a new set today. Any one have any outer ideas? I have checked injectors and looked for vac leaks also. Sorry this is sloppy stuff keeps jumping to mind.

 

All of the symptoms you've described point to the fuel pump like you suspected. It's all guesswork until you get a fuel pressure tester on it.