Im sure the basics of the topic have been covered before, but in the interest of saving a little time doing the search and sifting through a bunch of responses, I thought I would ask.

I have been trying to teach myself this method of shooting.  I am a mathematician by trade and would love to add a little more insurance to my style of shooting.  I know that at 10 yards by gap is 17" and at 20 yards it is 26"  At 30 yards it is 27" and at 40 yards it is about 19".  If I were to use strictly gap shooting I know with my right eye closed I have to shoot about 12" right of the target and use those gaps to get good results.
Now with the hill split vision style am I still using those same gaps or do I change my gaps to where I see the arrow out of focus with both eyes open?

I'm not following why your closing your right eye.
Are you shooting left handed and right eye dominant ?

Also your gaps  seem a little confusing.

Both eyes should be open. Without looking at the end of the arrow you should pick it up and it should be centered  and at the distance your gap is. Sounds like you have most of this figured out.

In my opinion gap shoot is great for winning z3 D tournaments.
But for hunting more instinctive aiming works better at least for most guys.
I think as gap shooters get used to gaping most are going more in the instinctive while hunting.

You can gap shoot and cant your bow. Sounds like it needs to be canted so your eye is over the arrow. That may solve the right to left problem.

If you persue gap shooting you will need to reduce your gaps. You can raise your anchor, go to 3 under, shoot a longer arrow or a combination of these. You will need to be in the 25-35 yard point on range or shorter.

Im a gapper. From 15-25 yards my gap is about 24" below the target. I use the same gap for all these ranges. I hit an inch or so high or low depending on the distance. At 10 and 30 my gap is about 18". At 10 yards the arrow is still rising in it's arch trajectory. At 30 it is falling but they tend to hit in the same place. This simplifies things I only need to remember two gaps for 10-30 yards. My point on is 40 yards. I place the arrow tip on a deers hooves for the 24" gap and just below the elbow if you will for 10 and 30. Learned this from a Jimmy Blackmon video on gap shooting. Works great. I shoot split finger with my middle finger as my corn of mouth anchor.

Dustin, tried to send you an e-mail. Let me know if you got it.

Dustin your gaps should not change, I shoot a gap style now with one eye open only due to poor vision up close and trying to get a precise sight picture. Your aiming 12" to the right worries me that you may be overdrawing to the side of your face. Try to draw to the frt of your face with the arrow under your dominant eye to help this.