I would still use the "Not Present" trigger, but just make sure its not covering the whole map.
From what I've seen, the bad uses of the "Not Present" trigger are when the trigger covers an insane amount of area (ie: the whole island), or includes large areas that aren't relevant to the objectives.
If you make the trigger cover
only the objective-relevant area (town, base, etc) then...
1. You still force the player to be thorough
2. You do so without making them work unnecessarily hard
3. The objectives of completely taking an area remain valid
I would hate to have a mission that says "you have to storm this base .... and make sure you kill
most of the guys there".
The danger with ending a mission with a set number remaining (ie: 5) is that if you're in a firefight, and you hit that lower limit with other enemies in sight, its going to feel like a bug instead of an intentional design.
Hope this helps.