I play it that the monsters are but servants of Morcar/Zargon and not remotely controlled mindless pawns. So occasionally- goblins flee, zombies walk into pits and champions take on the strongest hero to prove their worth etc. But the monsters always bear the heroes ill will and I won't stop them from killing when the opportunity arises (that would tip the balance from a game to a story).
Considering the points above though, hiding is perhaps too much different from HQ style and more D&D. I wondered for a bit whether invisible heroes could note their location in their heads so that the GM is actually unaware of where they are until they open doors or reveal new sections of the dungeon. The only problem I see with this is that you wouldn't know when to activate traps, the only solution would be to leave those traps undiscovered. It's all a bit tricky.
I might try to cast a crystal resin wizard to represent invisibility













