I agree with John's thinking as to the geometry though not necessarily for the same reasons. I'm just not crazy about the 45° particularly with only 4 rings
Try experimenting with 22.5° or 60°. I think you are going to like either of those angles especially if you move to a six ring knot. I suspect it will not be necessary to use scroll saw cuts for your rings.......bandsaw thickness should be just fine. Now if you go to eight rings, then the scroll saw might be the choice??