Have you compared hand calculated numbers (miles/gallons) to computer's result? I can't think of a good reason for mileage to truly depend on tank content, so it would be a good idea to test the hypothesis that the numbers on the readout are incorrect. Next time you start with a full tank, drive 200 miles and record both the display readout and the hand calc. Fill the same way and repeat at 400 and 600 miles to check for any trend with respect to accuracy. After you do this (or maybe before, but obviously not at the same time) you might want to do the same test for filling up the tube vs. letting the pump cut off on its own. If there is a difference, maybe something screwy is going on when you overfill the tank.

Good luck!