EDIT, ok so I think it could be the brakes dragging, couldn't get it to do it if I hadn't touched the brakes. Then it also did the same thing pulling in forward. Thinking my vacuum booster is going and the brakes are releasing only when the booster looses vacuum.

OK so '87 F-350 460 C6 4WD, Yeah I know '87 this is an '80-'86 section but the only difference is body style. Mechanically my truck has much more in common with the '80-'86 trucks then the '87-'96 trucks.

When I back in at home it's on a slight up hill grade, all is good, back in, put it in park, etc. Then I shut off the engine and the truck rolls forward downhill like something released. It's like the reverse is dragging holding the truck back until the engine stops and thus the pump stops. Does this happen, if so how, what do I do about it, and is it also dragging while driving forward?

I know quite a bit about my truck/vehicles but auto trannies are the last black art I'm not proficient in. That said assuming the C6 uses a reverse band it seams only logical to assume this band is dragging. And sence it releases when the pump stops that the issue isn't with the band but with the valve body not shutting off pressure to the piston for the band completely.

Also posted in the tranny section here: https://www.ford-trucks.com/forums/11...l#post12161796 And the '87-'96 Section here: https://www.ford-trucks.com/forums/1...l#post12161816

 

I'm by no means a transmission guru but, it sounds like your trans is not going into park. Could be the linkage or a problem with the trans.
Have you tried giving it gas while in park?

 

All other indications are that it goes into park completely, I feel the detent, the majority of the reward force releasees, the engine speeds up and more throttle only revs the engine.

 

Sounds to me like the parking pawl.

https://www.google.com/search?q=park...w=1615&bih=819

 

It rolls just a little until catching the pawl, if everything was fine except the pawl wouldn't it roll in park with the engine running? It rolls only after the engine is shut off.

 

Does it do it on a flat surface too?

The one in my '86 has been doing this from the day I got it, not worried about it. Just need to park a foot back from things. Shifts fine, fluid is staying nice and red. Not sure what it is. Also does it if pulling forward into a parking spot.

 

Don't see how I would notice it on a flat surface.

I worry for 2 reasons, could be killing my MPG and could be wearing out my reverse band.

 

Only one (intermediate) band is used in the C6 transmission.
No reverse band.

 

Just saw your edit on the OP, heres how I'd check that theory... engine running, park on a hill, then pull the vac. line from the booster, see if it rolls forward against the park pawl. You could do it in nuetral if you have a helper in the truck or dont mind letting it roll down the hill on its own.