I think my Mrs is angling for me to have a music room when we move - I must say she has been beyond tolerant when it comes to hifi coming and going... Never given me any serious grief!

To be fair, I've never had grief from Ruth although she stops short of calling my speakers 'beautiful'

A couple questions about this design. You say NVA inspired, so have you used a simple capacitor in place of crossover or applied doping to the bass driver? This is an interesting concept (floor standing cube?). I really dislike stand mounts now and fail to see their point given they don't actually save space and often cost as much.

Classicrock...

There are three inspirations for this design:

1. The shape is based on the Larson Pyramid omni-directional speaker that was produced from the late '60s to early '70s.

2. The internals are a quarter-wave, folded, expanding transmission line that is based on the 1930s work of Paul Voigt and more recently, Martin J King, quarter-wave.com, and the late Terry Cain in the USA, plus some helpful input from Scott Lindgren of Woden Designs/Reiver Acoustics.
They are a development of my earlier open-source "Metronome" design, which is an straight up, quarter wave expanding transmission line, the biggest of which I had at home, stood five feet tall. Details of this design, plus suggestions for cabinets and drivers can be found here...  www.frugal-horn.com/metronome.html

3. Richard Dunn's NVA Cube, semi-omnidirectional that uses the rear wall and ceiling, to reflect part of the soundfield and uses the room acoustics, rather than trying to fight them

I was looking for a way to fold a Metronome speaker in two by folding the internal transmission line, to reduce the height without compromising the sound quality.
There were two difficulties with this:

first, the transmission line tapers in two directions, making the act of folding it and maintaining the bi-directional taper extremely awkward.
Second, in order for the quarter wave resonator to work properly, the main driver has to be half way along the line, which made, folding the line and mounting the driver on the front of the cabinet another pain.
If I wanted to keep the pure geometry of the external shape, then all sorts of compound angled panels would have had to have been designed and fitted into the cabinet to internally shorten the rear part of the line to take into account the additional distance across the cabinet top so as to get the driver half way along.
Now that is a doddle with your average transmission line speaker, such as IPL, PMC etc because the cab is rectangular and it only takes two internal panels to achieve correct driver positioning and correct taper. To do the same with a pyramidal shape cabinet takes four panels.

Here's why:
By folding a line inside a pyramidal shape we create a problem that a straight rectangular cab does not have.
The exit port for the line emerges at floor level, in order to provide bass reinforcement. Now...looking downwards from the top, the half of the line that heads towards the floor, has a natural expansion provided by the sloping sides of the pyramid, so a suitably shaped internal panel neatly divides the cab in two, and expansion is assured...easy!

Ah but now, with the driver on the front, we already have a problem in that it is not half way along the line:
A) due to it being on the front.
B) due to the distance along the top of the cab towards the rear, adding to the rear length and putting the driver nearer to the line exit than the start.
So that can be solved by putting a horizontal internal panel in the rear half of the line, to shorten the back part and bring the driver to the half way position. Due to the pyramid shape we now need to put an angle on three of the edges of the horizontal divider.

OK so now the driver is half way along the line...oh goody...now we have another problem and this is a biggie.
Remember the front half of the line going down to the port? Yes that expands downwards nicely.
But what about the rear half of the line where it travels upwards from the base towards the internal surface of the cabinet top?
That is CONTRACTING as it goes upwards....so to make it expand at the correct rate we need another two internal panels that form a short upward pointing straight sided horn. The panels need compound angles on both ends. So now I'm losing the will to live. This internally  folded pyramid lark is rapidly turning into more trouble than it's worth.

I was ready to abandon the whole thing, and then I noticed the NVA Cube......BINGO, EUREKA and all that jazz.

Place the main driver on the top of the cabinet, and it naturally falls half way along the transmission line. Now we only need three internal panels to divide the cab, provide an upward expansion; no horizontal. Put the upward expansion panels at the inside of the front face and we can send the downward expansion to the back and get the port near the rear floor wall junction, put the tweeter on the front to get better localisation cues and Bob's your uncle.

So to answer your question: yes the design fell into place when it hit me that the driver orientation of the NVA Cube, would solve the seemingly insurmountable problems the design presented, but it is not a floorstanding Cube internally.
The drivers are not doped, but the "crossover" is indeed a simple cap that protects the tweeter.

The NVA Cube, driver config was the final piece of the jigsaw. Without it, this design would not have got off the drawing board.

Yep,
The things may look outwardly simple, and the actual implementation of driver configuration, complete with simple cap crossover was fairly easy to get working optimally.
This was because the main driver was chosen for its even midrange response coupled with a nice 6dB/octave off axis rolldown above 5Khz. The tweeter was rolled in at the same rate, with the cap, to produce an even response.
The bass is boosted by the near wall placement and of course, the near wall placement required for the semi-omni operation complements the wall placement required by the bass end: synergy in its purest form.
The whole thing was able to be designed as a system, once I had hit upon and realised that although RD's speaker is a completely different animal, the NVA Cube's driver config was the perfect way to go.
As for the cabinetry, needed to pull it all together....well you've read above about that blasted conundrum 

BTW I like the idea of your latest design. Sounds like it has great potential for a superb musical experience, and that's what it's all about.