Where I disagree with you is the reason for having lift of up to .50d(or any value greater than .25d) . I don't believe that much, if any, piston bounce occurs during the time a projectile is in the barrel because you have so much force constantly being applied from the pressure pushing the piston ...

For a 4" piston, you should aim to have it moving back only 1". If you have lathes and such to meet closer tolerances, you can reduce the pilot volume even more to have faster actuation time (its generally diameter/4 for pilot volume)

Worth clarifying that the piston needs only to move back ...

I can't say for sure if anyone else has actually tested the cracking pressure of a schrader with reasonably accurate equipment.

I have. :) (6" test gauge with parallax dial, calibrated within .25 of 1%)

It took 70psi to open the schrader using pressure alone.

This would mean that there would be ...

My .02 :)

In the search for increased efficiency, controlling air flow within the valve is a worthwhile idea.

I use a "floating o-ring" on the piston for my copper gun. It is simply a slightly loose o-ring groove with a hole drilled into the side of the piston.

The drilled hole is half in, and ...