Our out door cat can be a pain but we don't let him out at night intentionally (too many owls in the neighborhood) so we do encourage him to be outside during the day. And we can do two door separation but he's learned to throw himself against things downstairs too which sometimes wakes us up. It was pretty bad in January (cat mating season) and now that spring has sprung it's getting weird again. and he is neutered but still, it's my opinion he has a girl friend, maybe a bobcat.
We are up to four cats now, one must die somehow soon or I will have to take matters into my own hands.