how can I make the back wall transparent?

Have u looked thru the virtual systems for ideas?
In my case; room is 12 x 16 feet, speakers are 3' from wall; toe-in made a great increase in soundstage plus I'm using an equilateral triangle method. As in many of the virtual systems, I used bass traps in corners and 2 vertical DIY vertical panels on wall behind speakers; that wall then disappeared and became like a concert hall.
BUT, the panels are ugly...2 inch foam, mounted on boards that I can stow away when I have visitors. Obviously I'm not married.

"the acoustic designers I consulted seemed to feel that unless one uses massive amounts of bass trapping behind the listening position, one can't effectively ameliorate the total adverse influence of the rear wall."
I am using bass trapping panels and it works for me; in a small room you don't need massive amounts.

Achieving so much benefit from treatment in the upper 15"-24' of the room is what surprised me the most.

That's the way Peter(Pbnaudio) treated his rear wall; absorption along the entire upper wall. It's even more effective in his case since he has space between his listening position and the wall.

I'd like to do that, but my setup is in a living room.

Open question...Williewonka's use of a vinyl material is resulting in diffusion of sound waves, yes?
Then shouldn't the material have folds in it, otherwise it could be reflective?

I'm thinking if used in my room, vinyl would cause deflection of sound waves.

Many thanks, williewonka, I appreciate you sharing your research.
I did not realize that vinyl could absorb sound waves.

I've seen some types of acoustic curtains, as one of your links points out, they are made of fabric with a vinyl layer. But what is interesting to me is a roll of MVL and using it at the top of the wall where it meets the ceiling.
I have a tapestry on the wall behind my listening position and a vertical acoustic panel to right of it in the corner. The only problem is making this vinyl strip look aesthetically acceptable.

I was also wondering if I could use vinyl as a type of crown moulding behind me.

Nicely done, williewonka. Sounds like it matches the decor of the room as well.

When I referred to a "type of crown moulding, " I was wondering if there was a way to use a strip of thick vinyl near the ceiling where typical crown moulding is always placed. That's an open area for high frequency wave reflection.
I've been reading that MLV is used in sound proofing, and I need either absorption or diffusion.

I may experiment with some fabric across the ceiling area first, just to see what it looks like.

williewonka, that's the idea I had for an acoustic Crown Moulding.
I was thinking of mounting a 2x4" length of wood as the foundation, and that's about as far as I got.  I read that 1/8" MLV weighs 1 pound per sq. foot, then I googled "vinyl upholstery" and there are many options.

I appreciate the photo and all the info you've provided.