What if you just make the time to open the stash more if you've recently taken damage? It would definitely be better than getting the annoying "you've recently been in a fight" message.
Or better yet, if hiding from cops is the main issue, make a system where if a cop is in the vicinity of a player using a stash they can also access said players stash. I understand that might be a complicated system to implement but RP wise it makes alot of sense and it makes people think before trying to stash an item cause said stash could have more incriminating items in it. Give the opportunity for people to escape, and the opportunity for police to investigate