Well good....I'm glad your PJ option is open.
Your Screen Frame design will have to meet certain criteria if your to have LED Lighting, but I cannot see either the purpose or need to place the Screen assembly 4"to 6"off the wall. A normal Spandex Screen Frame of the size your envisioning is just under 3" deep. when one uses 1x3 Lumber for the Exterior Frame. For your purposed LED lighting, you'll need 1x4 Lumber for the Exterior Frame, overlaid with 1x2 set Flat and forward to the leading edge of the 1x4 Frame,
This is because the 1x4 Frame MUST sit flush against the Wall to prevent light leakage behind the Screen itself. The good news is that the most accepted mounting method for the Screen (A Ripped 1x8 Wood French Cleat) does exactly that...pulls the Screen frame tightly against the wall.
I can provide a detailed Drawing of the Frame construction, w/measurements...along with a needed list of the specific materials...if you'd like me to.
Projector-wise, choosing the Epson 5050ub would be a "prefect world" choice. Set at a 16' Throw, it would deliver a 4K (EShift) 135" diagonal image that would reach up to 30 fl on Spandex. A 13'-8" Throw (shortest advisable) would garner you 33 fl. Either way...your back up to your desired 135" size.
However (...there just had to be a "However"...) if it was possible to relocate the Bar so that the front seating was closer to the Front Wall, a 120" image would be considerably more in keeping with getting excellent HDR. 38 fl. at 14' Throw....much better all around, and the closer in viewing point allows the 120"er to have exactly the same impact as a 135" would when seated further back.
Or...moving closer can make the 135"er look like a 150"er! Closer is better for several different reasons beside the Projector's ability to deliver a dynamic Image alone.
Size matters...but too often seems to be the only criteria people use when designing their Theaters. Again....coming in late in the game doesn't let me suggest a lot more that "what ifs" and "it would be better to'"....things that can be disallowed all to easily at this juncture.
But let me add this. The positioning of your Surrounds and Atmos drivers become all the more easier, and the end aural results all the more better in a collapsed Floor Plan. Your Theater is significantly longer (deeper) than it is wide across the Front Sound Stage...and that affects every aspect of performance.
- Sound Stage Imaging (relates to Surround and Atmos positioning)
- Volume potentially needed
- Acoustic considerations (relates to Volume requirements)
- Image size requirements to make for a "Theater-Like" environment.(relates to visual quality and dynamics)
Now you can ignore all that and still be happy with the end results....but happy doesn't equate to being ecstatic, or amazed. And at this point in time you are still well situated for creating amazing end results. Will that happen? S'up to you to decide.