McDave: Interesting machination. I've never had much difficulty judging the arrow point vis-a-vis the string with the bow held vertically as you described in your first post. Rather than hold it in my hand, I hang the bow (with an arrow nocked) from a peg and then stand behind the bow and sight down the string/arrow.
That being said, your way of aligning and measuring the amount of the offset no doubt works, but what does it tell you? The measurement in inches gives a false sense of preciseness. That is, you have a precise measurement, but you don't know if the arrow point is in the right place or not. I suppose a lot of trial and error would eventually come up with the best distance for your bow/arrow combination. Once determined, you would have a precise reference point for that particular arrow/bow, but it would likely not be accurate for a longer, shorter, thicker, thinner arrow, etc. or for someone with a different shooting form.
In truth, as you suggest, I suspect there's a range of space (from the arrow tip partially bisecting the string to resting outside of it) that will work. And, given that "more than one setting" will work so to speak, preciseness isn't really necessary.
In fact, when you have the bow set up for your measurement, if you just got behind the string at eye level and eyeballed it, I think you would get a sufficient picture. Your system takes bow movement out of the equation and pre aligns the string with the center of the bow, thus making it easier to get a clearer view of the relationship of the arrow point to the string (much as hanging the bow vertically from a peg does). But I don't think that relationship necessarily needs to be expressed in inches and fractions thereof.
As per your question, I think it may be a solution in search of a problem, but it's fun thinking about these kinds of things.