Since the remotes are IR you pretty much need line of sight so you would have to be aiming the remote through the door glass. If that is a hallway I suspect that anyone using the remote will be aiming it at the TV in the room not at the door.
1000 sqf is relatively crammed, u may encounter remote interference issue. Close doors to the rooms?
Yes. That is my fear. We thought about alternating brands of TVs so, rooms 1, 3, 5, 7 have a Samsung and 2, 4, 6, 8 have a Vizio or whatever... The doors would probably be shut but there is a glass window on each door FWIW.