TL;DR: It was a loose positive battery terminal

Long version:

Last month my son bought a roughly used 2005 GT with 177k miles on it. In another looong post we first attacked a clutch problem (which turned out to be the pedal linkage - $12 fix).

This past weekend, it was on to the DTCs. It ran, but roughly, especially at hot idle (yes, yes, cam phasers, but actually not -...

2005 GT with P0161, P0171, P0174, P0345, P0463, P2270 solved with this "one weird trick!"