There are a few things that you MUST do to that room, otherwise it will have potentially horrible acoustics.
1) First, is install a plywood floor on rubber mats, otherwise your vibs will be zero. Then you build the wood frames onto the plywood, this will help with soundproofing. Concrete transmits impact noise with zero loss, as if it were paper thin.
You'll have to place rubber mating or iso clips on all points contacting the concrete (all joists etc).
It's important that no concrete nailers or screws are used to that aren't isolated.
2) Secondly, is not putting up any drywall in the ceiling and upper half of the walls. It's a waste of space and is weak.
This should all be OSB and it should be in a checkerboard pattern. 50% raw insulation and 50% OSB in standard-width squares. This should then be covered with black fabric (think acoustically-transparent speaker fabric.)
This will help tame the strong modes you'll have throughout the entire frequency band from 20hz up. It also means you won't be wasting additional money and space on acoustical panels later on.
OSB is great because you don't need to seek for stud alignment when mounting stuff onto it.
3) The projector screen and mount must be directly attached to the concrete. If you are like the rest of the members here, the bass will vibrate a wood frame to pieces, which will blur the screen.
My room being an all-wood design has this problem. Don't make the mistakes I did.
4) Run all cables through flex pipe or PVC. Overtime cables oxidize and will need replacing, and new cabling technology (like optical data, which may or may not be HDMI anymore) will be required.
5) I'm not sure if that duct will act in an IB-like fashion. It will behave like ported-IB. I would still put subwoofers up there though...
Place them on the OSB squares, and then you'd have to build OSB insets for the absorbing sections obviously, as IB requires containment. A lot of work, but probably well worth it.
I'd also shorten those air vents to the smallest possible length on the HT-side. Build the muffling box on the outside. That will increase inefficiency and reduce rattling and wasted ceiling space that could be used for IB air or impact-noise isolation.
The PA-460 loves large IB-sized boxes, and they are dirt-cheap and ultra-high efficiency. Several people are tuning them to 20hz. Another option would be FI IB-18's, depending on mounting-depth you may have to lower the ceiling a few inches.
As long as it is higher than 6'8" I don't think anyone other than basketball players will be banging their heads, obviously a full 8 feet would be best.
6) The projector and lights and low-power rack equipment can share a dedicated breaker and it should be on online-UPS puresine powered to avoid blinking lights every time the bass hits, and to avoid burning out the projector bulb during any given inevitable power-outage, and to keep your sources on (to avoid sudden turn-off popping sounds), and to keep you from being in the dark during exiting.
I recommend these line-interactive units, they are cheap and they work:
SurgeX for advanced surge and continuous-overvoltage protection:
I know all of this is highly unconventional, but regular rooms don't take acoustics and HT requirements into consideration, especially ones gear for extreme-systems, and 99.999% of contractors have no experience building such rooms (and even fewer, "living with" the results of their work forever...)
Somethings to consider anyway, it might already be "too-late..."