That approach makes no sense at all to me. Does it have cam and crank timing synchronization? If so, the cam and crank relationship is fine. I could see pulling the #1 injector, and putting in a depth gauge to find tdc, then comparing it with the cam timing if that is a problem. The head would not need to come off for this. I'd start with a relative compression test. If that's messed up in any way, or the engine rolls over too freely, then on to mechanical compression check. That's a very non-intrusive test, and only takes 3 billable hours. If you have a compression problem on any cylinder, you pull said valve cover, and inspect for visible valve train damage. If none is found, you do a leak down test. If that fails, then you pull a head and see.
So what exactly has the dealership done for $6200? Sounds like you need to put the screws to the service manager, and hold them accountable for proper diagnostics. You might be surprised how much they'll work to resolve your concern if call ford HQ with your situation on the gross incompetence. This is, assuming you do it level headed, and present fact based concerns. They also have access to an FSE (Field service engineer) for escalated problems, where the engineer comes down to make sure things are being done right. In the dealership I work at, if you do unnecessary diagnostics because of incompetence, you don't get paid. All labor and parts need to be justified. If you want any extra help on this, pm me your number, and I'll do my best to help figure out what this needs.
