New engine seems a bit over the top. Assuming your oil pressure is normal, and compression is good.
Sludge, if that really is what is causing the problem can cause one or both of the VCT's or VCT solenoids to malfunction if the oil passageways are clogged. Think you're on the right track suspecting the solenoid, and if it were mine, I'd start there on bank 2 since it's easy to pull and inspect.
Episode 22 at the following link has some good info regarding the VCT on our trucks.