I looked up the noise levels specs on the optoma uhz65 laser and jvc Nx7 on HDR high. It seems like the JVC is still slightly quieter (31dB) vs optoma (33dB).
Looked up the noise specs on aircon FCU…starmex says their silent mode is the quietest at ~21dB. While the normal modes typically start at ~30ish dB.
That means that without jumping through inordinate amount of hoops, the room noise floor is limited to 30dB +.
To break that limit would be exponentially more expensive - ducted FCU with separate, silenced, oversized inlet and return air ducting. Otherwise airflow itself generates noise. The supply and return air ducts themselves are huge sources of noise leakage, so wherever the ducted FCU is placed, that room will be noisy and will need additional soundproofing, or otherwise limited in use. If its a common area, anyone in the common area will will listening to the movie, whether they like it or not.
Similarly for the projector hush box. Building a separate projection room is an option, and can house the rest of the noisy electronics. (currently I can hear the HDD reader head tracking and reading when I hit play on the zidoo, before the movie starts playing)
The projection /equipment room can then be the air space for IB subs, and the front baffle wall designed as bass traps. Though some, myself included, prefer to have the primary low and midbass subs firing from the front wall, together with the screen channels.