2003 F-150 Supercrew 4WD problems

My 03 FX-4 5.4L Supercrew has a problem. There are no error codes thrown.

Transfer case seems to engage just fine and the dash lights indicate that the system is engaged. There are no problems engaging 2H, 4H, or 4L. Except that once in awhile the front axle either mysteriously disengages or won't engage. And when this happens the system will not engage again until the truck has made a couple of tight turns on dry pavement. Which isn't always available obviously!

In the snow the 4WD only works about 95% of the time. I think that I isolated the problem to the front axle ESOF vacuum control solenoids and/or actuator this week, and $200 spent at the dealership to diagnose it says that there is "muck" (that was the term given) inside the vacuum system and they want to replace both solenoids and the actuator. However these items all three pass all of the Helm manual tests for voltage, resistance, and function while on the lift and I cannot hear see or feel anything like "muck" inside the system.

Today, I drove it for two hours on snow covered fire roads and it worked fine. Except twice. Two times the system failed to go from 2WD back into 4WD (but the dash lights indicated that the transfer case was engaged) and continued to refuse to turn over the front wheels until I finally exited to bare pavement and did a couple of hard turns, at which point the axle then dropped into 4WD just fine.

Any ideas on what this might be? I thought maybe it was a vacuum leak on the 4WD solenoid side of the system but all connections look good. If it is a vacuum loss it would have to be sporadic, which doesn't make much sense either.

I've now flushed the front axle oil twice with Mobil 1 75w90 synthetic, once at 30k miles and now again at 52k miles. There are no odd noises.

The problem has existed the whole time I have owned the truck which has been two years and 25k miles. Fortunately it doesn't snow all that much here.

I'm stumped.