McDave;
What I was thinking was if at closer range one had a gap of 1/2 " off of a rest and re-tuned to the shelf the arrow would would be lower, ergo the gap would be larger and the point distance on would - should increase.
True, the arrow would be lower on the shelf than it was on the rest, but your nocking point would be lower on the string by an equal amount, unless your nock height changed. You would be holding the whole bow 1/2” (or so) higher, but the relationship between the arrow and your eye would remain the same, unless you changed your anchor. Therefore, I would not expect to see much difference in point on.
I agree that this would be fun to test, and would be interested to see if your real-life results agree with my speculations.