Ford F-150 (2004-2008) :: 2006 - Missing And Rough Idle - Codes P0340 / P0344 / P0345 And P0349?

I recently purchased my first Ford pickup. I bought a 2006 F-150 with the 5.4L 3V engine. I have only driven it for about 300 miles so far and am having problems. The engine has 146,000 miles on it. I have read several posts on here about the cam phasers which I believe that I may have some issues with. The engine will run well when cold, on the road, etc. The engine does have a slight ticking after it warms up (cam phasers?). When I come to a stop after the engine is operating temperature, the engine will start to miss and shudder and all 4 above codes come active and are also pending (8 codes in total).

All 4 codes are logged at the same time. I have replaced both cam position sensors, both sensor ends and terminals for cam position sensors, checked wiring around the rear of engine (does not appear to be rubbed through), all plugs were replaced, and all COP boots are good. Is there anything that can cause these codes that may not be the actual cam position sensors, ie. VTC, COPs, cam phasers? What pins the cam position sensors come on the ECU (so I can ohm the entire wire harness)?

Also, if the engine is missing with the codes active and I rev the engine up it will come back to idle and run great. The engine never dies out, just runs horribly. I have also unplugged each sensor with the engine running which has no effect on the way it runs.