Yep, for that indoor space I would use a 2.8mm lens. It would let you see the whole room, and if you did want to mount it where you indicated with the red circles you could use the Corridor Mode nicely up there. It just wouldn't be so good up there in case someone wore a baseball cap.
Mine is mounted up there, but that is because it would be vulnerable from the blind area on it's left side. It's only got about 2ft thick Berberis Julianae and Pyracantha on that side. The right side has about 8 ft of Berberis Verruculosa to protect it. I guess there would be plenty of DNA left on the Berberis, so perhaps I should take a chill-pill on it and mount it lower. >}
Berberis Julianae
Berberis Verruculosa
In your situation they would have no option at all but to come at it from the front, and would be seen.