Dear Ron,
Sorry for the delay -- I've been puzzling over the problem.
The only thing that occurs to me to ask is whether your hands hang differently with a center-shafted putter versus a heel-shafted putter. Typically, the hands hang above the toes, while the shoulder sits above the balls of the feet. If the hands are in the same position above the toes for both putters, then the heel shafted putter should be more upright -- it's strictly trigonometry. The only way one putter gets flatter is when the hands are farther back from the ball or lower than otherwise.
On the other hand, the hosel of the center-shafted putter is farther from your hands than is the case with a heel-shafted putter. That means that the "hypotenuse" length of the center-shafted putter is longer than the "hypotenuse" length of the heel-shafted putter. If the hands are in the same position both times, and the ball is out from the toes the same position both times, then the hosels point at the ground two different distances out from the toes. The center-shafted hosel points at the ground right at the ball (7.75" out from the toes), but the heel-shafted hosel aims at the ground perhaps 2 inches short of the ball (5.75" out from the ball). This means that the handle meets the center of the hands 28.1" up from the center-shafted sole, but only 27.6" up from the heel-shafted sole. If you hold both putter handles in the same "middle of the grip," and also hang both arms the same way, then this forces you back from the heel-shafted putter, and this in turn "flattens" the heel-shafted putter more than the center-shafted putter.
My guess is that the laws of geometry are not changing, but instead you are not standing as close to the ball with the heel-shafted putter. In order for the lie angles to be the same, the distance from the hosel to your toes has to be the same, not the distance from ball to toes. If the lie angles are the same and your hand positions are the same in the way they hang and the way they are placed on the handle, then the heel-shafted putter will have a shorter total length.
Cheers!
Geoff Mangum
Putting Theorist and Coach
PuttingZone
http://puttingzone.com