So far spent missiles have not been requested too frequently in TBoAA. I can only remember it being requested twice, but it could have happened more.
For now, how about one fourth of the arrows that missed (round up if at x.5 or x.75)are still on the battlefield, instead of being shot out of the arena or broken? I will have to keep track in the future, if requested. You still have to pick them up.
In Paulina's case, we can just say that the misses are directly below where she fired them from, just to make it simple.