Ya, I thought about that too, you could just make it so the new arrows can't be picked up, or possibly you could attach a script to them so when they're picked up they turn back (I'm not sure exactly how you would do this though)
Attaching scripts to projectiles or targeting projectiles with scripts can not be done. Switching them out as suggested certainly can be, and it's relatively simple bit of scripting. But that breaks too when someone has arrows from another mod that you can't account for. Mods absolutely will add more arrows. Mystic Elven and Dragon Bone are two that come immediately to mind.
An alternative might be, given that this is for a Daedric Princes reward, to give the player bound arrows for the duration. Heck, you could even give them a bound bow (which automatically uses bound arrow projectiles).
There is another alternative that comes to mind that's close to your original idea to alter accuracy. Note that accuracy is not really an issue in this game. People already modify ini settings to get around auto aim issues and distance issues, so the only remaining one is moving targets. So you could script a slow time effect for when a bow is drawn, and release it when the bow is fired. Just a thought. That should be doable.