The only way I found to DEFINITIVELY troubleshoot a similar problem on my (now gone) '83 Tioga E-350 460 with Motorcraft/Holley 4V was to put a fuel pressure gauge on it where I could see it, and drive it. Observe the fuel pressure when it starts behaving badly. Mine dropped to 1 psi or less when it acted up.
Mine turned out to be the hot fuel diverter valve (the aluminum V Block that has fuel line in, and 2 fuel lines out - one to the carb and one back to the tank).
Prior to this, troubleshooting/futile swapping of good parts included replacing an electric fuel pump (it really went bad... the start of the misbehavior but coincidental), replacing the fuel filterS - yeah, plural ... including the brass strainer in the base of the carb), adding more fuel filters suspecting junk/gunk in the tank, removing, cleaning, reinstalling the fuel tank (didn't really need it).
In desperation, I added a mechanical fuel pump inline with the electric fuel pump (my electric was not in the tank, but external) which provided enough capacity to overcome the hot fuel diverter valve. Having said that, I sold it before replacing that valve. I still cannot say definitely that it was the sole source of the problem, but it's still what I point my finger towards.
Not sure how much of what I experienced with my 460 is relevant to your 351, but something to ponder or investigate. I also found a lot of good info on
Ford Trucks forums
'07 Ram 2500 CTD 4x4 Quad Cab
'10 Keystone Laredo 245 5er