Calvin, if you don't mind- I'm a bit curious as to how you determined the 0.0080" wear or gap at the hinge-- Harry's remarks about using brass shim stock is one very good way to go, having Larry Del Greco install a new hinge pin to 'size" is certainly another- it is also possible, in some cases, to rebuild the wear surface of the hinge pin with spray well and remachining- I have never removed a hinge pin from a Parker (or a Smith) but I believe the set screw is a LH thread (as you will find in the triiger housing group of a M12 for example)--
When you state "off face" did you mean when the forearm is removed with the gun cocked, you can "wiggle" the barrels slightly- another test is to then either mount it into your shoulder pocket with a bit of "ommph" or smack the buttplate/recoil pad to see if there is any laternal "shuck" or movement- if so, that might mean the bolt wear plate or wear in the doll's head area- hard to know for sure.
There are many very fine Parker gunsmiths extant, and thank the Lord for that- The "advantage" the Del Greco's have is the long generations of ties to the Parker gun and also their inventory of original Parker parts. Their reputation speaks for itself-- Best of luck with the repairs--