I been having a problem with my 2005 Ford.

I been having a problem with my 2005 Ford Expedition Eddie Bauer 5.4 L.

Engine suddenly starting running rough. Will only idol for a few minutes then start to stall. If you hold gas pedal down some, it will sound better but feels like a cylinder miss. Also motor sounds a little louder than previously.

Replaced fuel filter - no change to performance
Replaced all 8 spark plugs and boots/springs. - No change to performance
Did not change coil packs.

Scan code from local garage says advanced or retarded timing. My dumb fault I did not get the exact code from them. They said that oil sludge may be blocking a VCT solenoid and recommended a complete motor rebuild for $2500 to remove all oil sludge. I'm wasn't totally convinced that's the problem, but I did the following anyway.

I checked the resistance on both VCT solenoids and they both were 8.3 ohms. OK, I think, per other internet searches.

I then ran Gunk oil flush through motor for 5 minutes, replaced the oil and oil filter, per the instructions. I used Mobil synthetic oil.
Still no change to performance

I also read online that the tming chage could have jumped a tooth. How realistic is that to happen. Any ided what it may cost to have that fixed? Or could this be another issue?

Thanks,
Bob