I can see how sensitivity affects accuracy, but high accuracy isn't achieved from shooting static targets.
Agreed, thats why the targets move

LGS already does that, but you still have to experiment with dpi and in game sensitivity until you find what suits you. But once you do it saves it to the game profile and loads your dpi setting, macros, button assignments etc when you load the game.
edit - Also how does your solution differ from this?
http://ragial.com/mouse/
LGS lets you change your settings (As do many mouse applications) with a great degree of accuracy - but but its still up to the user to determine what those settings should be.
I fully accept that its my **** poor describing skills at work here, but people do not seem to be grasping what the app actually does. I'll try another way of explaining it.
Imagine you load up counter strike (Or any FPS game) and join a server with your friend. Your friend proceeds to run around, duck behind cover and generally try and make themselves difficult to hit for 1 minute. Your job is to keep your cross-hair on their face as best you can. You then make a note of how much of that minute your cross-hair was on their head (Estimated). You then adjust your sensitivity up or down a bit and do it again. If you kept your cross-hair on their head for more of the minute, then you again change the sensitivity in the same direction. If you were worse, you change it the other way. You keep repeating until you find the sensitivity you get the best "Cross hair on face" time with. This is then your best sensitivity. You make a note of this and use the same sensitivity in all FPS games. You do this by measuring with a ruler how far you move the mouse to turn 360 - you then use this measurement to set the sensitivity of your other games.
The only difference between this and my app are:
You use my game rather than counter-strike or whatever
Rather than a friends head, you have an AI target trying not to get hit
You don't have to estimate how accurate you are being, the game records it for you
You don't have to stop and adjust your sensitivity every minute - the game does it automatically.
(Maybe) You can export sensitivity settings to your games directly, rather than having to use a ruler to measure your mouse movement.
Hope that makes more sense - but let me know if anything is still unclear. Like I say, I think a video explanation would be better, will look at making one if I do go for greenlight.