If the orientation of your Ceiling Joists runs length-wise to your Screen wall, you can do what your considering.
Build a Plywood enclosure to the dimensions needed to enclose the screen assembly, with at least 2" on all "sides". If it (...the enclosure...) can be nailed or screwed to the Joist closest to the "Wall", of course that would be best.
Also, be sure it's placed 1/2" recessed (flush with the Joist) so you can easily wrap the edge of the Enclosure, giving it a "joint-less' appearance.
The "Side" and "Forward" edges of the Enclosure will need a "Nailer" ledge for the adjoining edges of Drywall to rest/be attached to.
Making "edge-less" corners isn't that difficult, but it does lend a smoothness and simplicity to what would otherwise be looked at as being "A Box" . The same idea for your "PJ Shadow Box" will leave you with a very clean look.
However, be advised that if you have not already settled on a PJ, you must take into account;
*the distance from the screen to the PJ's lens
*Desired Screen Size
*PJ's Luminosity (Lumens)
*Ambient Light Viewing circumstances.
*PJ ventilation needs/requirements
Some newer 1080p PJs both intake and exhaust air from the front. THAT is amount your most important considerations if you plan to shelf mount or recess the PJ in any manner or degree.
Your thoughts about "blending in" the Theater aspect into your living area are ones I've likewise shared for some time. I do of course cherish a well thought out dedicated Theater, but as more and more varied Folk catch the fever for the "Jetson Wall Vision" approach to daily viewing in Family Rooms / Morning Rooms, interacting with the WAF (Wife Acceptance Factor) on every possible Cosmetic / Aesthetic front only makes the satisfaction index for all parties all the more higher.
Much of what you are planning is beyond the scope of this particular"Screens" Forum, and the "Powers That Be" prefer that details on "Construction and DIY-ism" be directed to the appropriate Forums.
Home Theater Construction is one. However if you stop by on DIY Screens, you'll find some who are using the less expensive Electric Mfg Screens for paint palettes to ramp up performance. And the degree of DIY-ism on that Forum also will lend itself to you other related aspects.
I'll watch for you there....or PM me for more details/advice if you'd prefer.