I've been waitin' on you, GMMAT.
I could care less about "centering my pin" in my peep. It's unnecessary.
It's unnecessary because your eye does it for you.
In the other thread, you said:
I use a larger peep that aligns perfectly with my pin guard. I squint my left eye for just a slight moment upon reaching full draw.....kind of like centering a bubble on a level....to get the peep and the pin guard aligned.....and then it's eyes wide open (both). I never look back at either.....just the target and the pin (in that order of importance).
By your own admission, you never check back to see if the guard is still centered. Instead, you quite properly concentrate on the target and pin, in that order. So, after you've centered that pin guard and gone on to the pin you want to use, you have no idea what happens.
Unless you've gone to extremes and trained your eye to do something totally unnatural, that pin is centered in the peep when you aim.