Combat is not a single, uninterrupted step. It is made up of several phases, as outlined in the
rules.
In particular, as you point out, a legal time to play this would be after the
Hire the Monster step (it is not a Monster until it is hired). You could do it before the
Weapon Damage step, or if you wanted to make sure the monster was going to survive first, you could wait until after that step and do it before the
Monster Damage step, since the monster's Power would not usually matter in its survival in the previous step.
None of these uses require the Mischief card to be an interrupt, as it does not require interrupting an action or ability while it is resolving, but instead operates between steps.