your peep and sight should have nothing to do with you anchoring point.you hit your anchor and when you do you just open that eye and it should be looking through the peep.if it doesn't , you peep is in the wrong place.it's just like looking through a scope,when you throw you rifle up to you sholder and put you face down, the scope should be in perfect alinement with you eye.
try putting you bow up and draw and hit your cnchor,don't even try to look through the peep. just get the anchor and after you have that down,then get someone to move you peep to your eye.don't move you head or eye any at all.let them move it till you can see through it and then tie it in place and reajust you pins and that should solve the problem.

does your peep have a alining tube on it? if not you may have to get a peep with a tube.the tube keeps the peep turned to the right angle everytime.