Oh...I see and understand now that bu "The Large Portion of The Wall" you meant the side to the left of the Fur Down...which BTW means a Ceiling section that boxes in a HVAC or Framing abutment. I also see that your Floor plan is reversed.
Here is a quick diagram of a proposed framing idea. It is based upon Your not deciding to take down the existing Tray Ceiling, or re-work the Grid.
1. The Wall's "primary" Top Plate would butt against the Tray Ceiling. It would "toe in" across the bottom of the Furred Plenum, and be attached to the Right Side wall and the Left Side wall.
2 Additional Studs would be cut to insert through the Ceiling Tiles and be "screwed" to the Top Plate (...from Underneath...) and attached to the upper existing Ceiling either via direct screws into Ceiling Joists, or via the shown 2x4 Blocking running laterally with the Top Plate.
3. Your Ceiling Height dictates limitations as to Screen size, as does the presence of the Furred Plenum.
You rough layout showing the screen spanning almost the entire 13'+ width is optimistic, as your PJ does not do 2.39:1 very effectively, unless your willing to let the bottom of the Screen be at 12" from the Floor...and 9" from the Drop Ceiling to achieve a 60" x 107" 122" diagonal 16:9 image (...and let the Wall be the Black masking Trim...for a "Floating Screen"...)
Personally I think you should place your Seating closer than 14'-4". Something like 12' would allow a 98" diagonal Screen to look like a much Bigger screen....even 110" would look super immersive from 12'. Projector placement can be anywhere from 12'-6" back, but should be placed as close to 13'.....no further, so as to optimize Lumen Output.
If Your seating is at 12' and the PJ Lens at 13', it's all good! Sit back at 14'=4" and the PJ would either be in front of you and very predominant...or far enough back to affect overall performance.
Building a insert-able AV Box with adjustable shelves, on whose outside Trim is attached to the outside edge of the 3/4" Plywood enclosure, will allow you to simply insert it into a framed out, braced opening, letting the Trim cover the outside edges of the Hole, and if you make the reat of the equipment enclosure a "Screwed on Panel"...then if you need to do maintenance or any re-wiring, you can simply slide the Enclosure out and set it on the Floor, and also, the nice big hole allows you to get into and behind the newly made Partition Wall.
As stated previously, use Coarse Threaded Utility (3" Drywall) Screws to attach Studs to Top Plates and Walls. It makes for a super tight, "wiggle free" framing.
Lastly, you can extend some Horizontal 2x4 Braces back from the Wall Framing to the existing Exterior Wall every other 16" O.C. space, sandwiching the ends between to vertical 2x4 Blocks laid Flat and Glued/Screwed to the Exterior Wall. Do everything as I have suggested and the partition Wall will effectively be "Cowboy Proof"....as in tossin' a Cowboy against it.
Of course, all of the above is how I would personally consider doing it. But that's me, and wadda I know frum nuttin'?
If any of it helps you....consider the effort expended a early Christmas Present.....