RE: 2 or 3 anchor points?
If I'm understanding your post, you have a peep sight and a kisser. My suggestion would be to remove the kisser button andtouch the string to the center of your nose. When you put the kisser in the corner of your mouth it sounds like the peep is to far to the right (if your right handed) and you have to tilt your head to see through it. You should not tilt your head to fit the bow. Keep your head straight up and down and draw the bow back so that you can see through the peep without tilting your head and I'm guessing your kisser will be in a little from the corner of your mouth.
If you remove the kisser you will still have three anchor points;
1. knuckle below ear lobe
2. string on tip of nose
3. sight lined up in center of peep
Good luck