loss of power
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Don't know if this will help your problem, but this past summer I went on a service call for a 2013 E350 cutaway truck (FEDEX van). 5.4 3v engine. Giving all of the same issues. After testing everything possible and determining to be good. I guessed that it may be a loss of electrical power to the engine. I swapped out the battery. I reset the codes and all troubles went away. I need to say though, the battery that was in it tested good. It would turn engine over fine. Im still at a loss of why a new battery fixed all of the problems, however it did.