I suggested this already, but not in the "suggestion" forum, so here it goes.
A certain percentage of "will not resign" FAs will actually resign with you at a price of 1.5x their "normal" asking price.
I.E. A guy who says "with FA pending, I'm going to test the open market" and then goes to the open market seeking $9M per year, will have, say, a 50% chance of saying "I'll resign, but only at $13.5M per year." You might still have a 50% chance of keeping your player, but you don't get the hometown discount. The probability could be random, or based on OVR, or an individual rating such as patience or makeup.