Are the same specific arrows hitting high every time and a different set of arrows hitting low every time? If yes, you have narrowed it down... maybe different field point weights or arrow weights / spine.
If this is a potential problem, number your arrows and see if the same arrows shoot high/low etc. then you'll know it's your arrows and it will relate to tip weight, vane orientation to the rest etc.
As for your peep, I see a lot of peeps served in with two servings, one above and one below the peep both the prep and the servings can"feel" tight but still be slipping and it doesn't take much to cause what you are describing. The solution to this problem is to do a continues serving starting at the top or the bottom you make your first serving then wrap it around one of the splits in the bow string, make a wrap or two around the peep itself and continue up the opposite side if the split then make your other serving. The peep cannot move when done this way. Good luck