2009 Ford F150 5.4L Engine P0022 Code: Idle Problems After Warm-Up Fixed?

I own a 2009 Ford F150 5.4L Triton with 138,000 miles that consistently shows the P0022 diagnostic trouble code. The truck runs smoothly when cold but begins to run poorly at idle or during stop lights once it heats up. When I shift into neutral and give it a slight throttle bump, the engine immediately runs smoothly again—only to fail the same way at the next stop light. Notably, removing the VCT solenoids completely eliminates the issue, indicating that the problem lies within the Variable Cam Timing (VCT) system. I have already replaced the timing chain, guides, tensioners, oil pump, phasers, and both VCT solenoid units (twice), as well as the cam position sensors. The oil pan and screen were also cleaned. I use 5W20 synthetic motor oil with Motorcraft Filer. Despite researching extensively, I’ve found many users reporting this same symptom but no definitive solutions. Has anyone successfully resolved this P0022 issue on a 2009 F150 5.4L? Any insights or repair steps would be greatly appreciated.