for curiosities sake, i tried this today (new 3ds).
i tried it using 9 frames and if my math isn't wrong, i actually got a 6 frame delay.
target was 12677 - 9 = 12668 which is where i hit A and the battle started.
but i got the one that was supposed to appear at 12674, 6 frames away from where I hit A.
if i'm understanding the basics of this whole system right, with that kind of inconsistency, there's probably not a whole lot that can be done to improve this for fini, unless you can also let the overlay predict what kind of frame delay you're going to have to expect at a certain frame.