I do agree there needs to be a bit more to survivor missions to make them non-instantaneous. That said, I don't think waiting is the right solution; it would get tedious waiting with no way to influence how long the mission takes once started. I'd rather completion time be based on in-game actions; allot an amount of time for each stash room found, boss defeated and mission completed (i.e. the things you normally do anyway), and once enough of those have been done the mission completes.
As an added bonus to this, it means you can't exploit sunrise / nightfall to avoid waiting, which I can see being the most common response to having to wait anyway.