Welcome to the forums mharris
You will definately find that todays short axle bows are much easier to shoot with a lower anchor then the long axle bows.You should find yourself anchoring somewhere on your jawbone.This will also give you much more room for your site pins adjustment.
I have used the Fletcher(held on by 2 strands of string) and the Shurz-a-peep(3 strands) personally I liked the fletcher much better.If the string ever twisted I never had a problem looking into a string strand which is very annoying as it happens on the Shurz-a-peep.
I solved my problem a few years ago and put the No-Peep by timberline on.All my problems with peep were gone.It gave me a rock solid anchor,making my accuracy much improved and have no worries about the light coming through a small hole when needed when hunting.
I'd reccomend the NP to anyone who wants to get rid of all the headaches of Peeps