A mock bid might be amusing, but I doubt it would be very helpful given the animosity between the two groups. Both sides would probably try their best to skew the information by "bidding" something they wouldn't dream of doing, or vice versa. And a lot would probably just opt to ignore the whole thing on general principles, especially if USAPA were to run it. (I doubt the company is interested in spending the time, money and manpower to run it, either.)
Back in the late 80s, the brain trust at Crystal City decided to move all the MD-80 flying out of the west coast (i.e. PSA) and move 737s out there to replace the flying. They were confident that the PSA pilots would follow the airplane rather than endure ground school. What they ended up with was a HUGE training debacle because, for equal pay, the west pilots decided they would stay home and fly the Boeing. That would seem to somewhat support your theory.
However, a large amount of pilots from those same west coast bases also decided to commute east to fly the 767 to Europe once the LAX 767 base closed. They were following the money. I don't blame them. That seems to support the opinion of the east pilots, that pilots will go for the gold given the opportunity, commuting be da**ed.
I think that pilots will stick close to home if there is little effect on their paycheck, but endure a lot of inconvenience to jump to the left seat or do "premium" flying.
So addresses east or west of the Mississippi may have some effect, but it would not be the overriding factor, IMHO. And we will never see a mock bid run at the company expense, or an effective mock bid run by USAPA.