Anyway, so I killed him, got the reward, and started resting to pseudo-ID it. I definitely got the "You are no longer very accurate" message that indicates that Divine Aim has worn off. And yet, when I go to fight more enemies, every hit is a *GREAT* hit...
Recasting the spell and letting it wear off doesn't seem to do anything either. I went up to the wilderness and rested for 1000 turns...still *GREAT*ing everything I touch. My paladin's turned into a Cuisinart.

Edit: as noted a couple posts below, the crit boost did eventually go away; just much, much later than it should have.