how can I make the back wall transparent?

The only way really is to use speakers that are bi-directional, like Magnepan planars for example, or omnidirectional. Front ported or acoustic suspension speaker designs, ie those where most or all sound is emitted from the front, will be most problematic.

Then it is a matter of getting enough distance between speakers and rear wall for proper timing of spatial queues (usually a few feet minimum) along with a good balance level between the direct and reflected sound that reaches your ears. That is determined mainly by distance from wall and db level of rear emitted sound, ie that reflected off rear wall. More distance to rear wall will require higher db of reflected sound to produce illusion of extending past rear wall. That is why bidirectional or omni speakers tend to do this best.

YEs, I mean wall behind speakers opposite from listening position, which is the one in front of you when listening facing speakers.

You can use room acoustics or fight them. Both are valid approaches. Each might have a better chance of success depending on magnitude and nature of room acoustics. All rooms have a unique sound and best to first assess it then use it and tweak accordingly as needed IMHO.

I think you've got it covered.

One thing worth adding is that you might have to adjust distance between speakers as well when you play with distance from front wall in order to maintain good imaging, including a strong center image in particular. Mono recordings are particularly useful for testing to see how well center imaging is doing. If center imaging works well for a mono recording, stereo recordings should benefit as well.

Its also worth noting that what works best for sound stage size and imaging may not be exactly the same setup that works best for flat frequency response top to bottom. I like to get the soundstage and imaging right first, then tweak from there as needed to get tonality right as needed. That might include wall treatments, or any of the usual suspects used to tweak sound quality from there.

The toilet paper rolls will only help with soundstage depth/making the back wall transparent if attenuation of sound levels to rear of speakers is what is called for based on all the above.

In terms of aesthetics, they is what they is. :^)

Glad to hear the happy ending.

So substitute for determination and trial and error over time when it comes to managing room acoustics. So many ways to skin the cat.