buck,
I'll give this a shot but in typical coach fashion, allow me to go the long way around the barn. When I am teaching someone that has problems with hitting left (right handed shooter) but otherwise appears to have pretty good (and repeatable)form, I will have them draw so they CAN see the string as a "big blurry blob (BBB)" right in front of their eye. I then have them place that "BBB" on the inside of their sight cutout window on their bow. That will give them an alignment of the arrow to the target and goes a long way to eliminating the "windage" problem.
After a while, you will no longer notice the string as it will become part of your "sight picture (whatever it is).
What I believe, without seeing you shoot, is that your newer style of canting the bow is giving you better alignment and placing the nock of the arrow under your eye better than what you were doing before. Many shooters can shoot very well with the nock to the right (again right handed shooter) of their eye (more on the outside of their face) but it is really one of those accommodations that folks make that really just makes the shot harder than it needs to be. That does NOT make it wrong, it just adds another dimension.
When you are just starting out try to be aware of the string but as you get comfortable with it, you will be aware of the string without taking any notice of it. I've claimed many times that at full draw, alignment is critical! 1/8 inch deviation of the nock at anchor can and will be responsible for about an 8 inch deviation of the arrow at 20 yards. Getting that string in front of your eye OR getting that arrow nock DIRECTLY under your eye does many good things for your accuracy and NOTHING bad.