You are working too hard - but I like it! As a Marine Artilleryman, I sort of appreciate that type of basic math, but I like speed even more!
I recommend you look up "Dead On Rangefinder", I use the principle of that device on my riser for a very quick range reference. The gist of this system is that you know the relative size of the animal you want to shoot. Where I hunt, most deer are ~14" from the bottom of their belly to the top of their back. This doesn't change all that much (you can adjust this to suit the animals in your area), and minor differences in this measurement don't matter all that much for hunting distances - after all, while I aim for a deliberate 'spot' to hit, I have about an 8" area that will still be effective. Enough of that...
Go to a measured distance that you normally expect to achieve a hunting shot, for me it is 20 yards. Put a marker at this distance that corresponds with your animal's measurement. For me, I cut a cardboard box exactly 14" and set it at the end of the 20yard distance. Walk back to your start point so you are 20 yards from that 14" box and hold your bow out as if shooting next to it. Mark on the face of your riser the top and bottom of that 14" piece of cardboard. Be as accurate as your dadgum steady arm will allow. Here is the magic - if a deer walks close to my stand, as I get ready to shoot, I can move my bow a matter of inches to align the two marks with the top and belly of the deer. Assuming the deer fits the 14" average, if the deer is larger than the span of these two marks it is closer than 20 yards, if it is smaller that the two marks, it is obviously farther away.
Put as many marks on your bow as you deem necessary to correspond with other ranges - or different color marks to account for different species (deer/turkey/bear/clowns - whatever you are hunting)
I hunt exclusively with a recurve, and I gap shoot for targets. Why is this relevant? Because on my hunting riser I put a 1/8" strip of white electrical tape on the face of my riser that corresponds with my 20 yard gap. It is dead nuts. This strip of tape is what I align with the belly of a deer therefore I only need one other mark to account for a deer at 20 yards. I personally like a 30 yard mark as well because that is my self-imposed hunting distance. It sucks when they are 'just' smaller than that mark...
Make sense? I think you'll like it because it leaves both hands free to shoot - and takes the math step out of the woods.