Waveguide complete, unintentionally matching the ASR panther color.
I've built the waveguide from a board of high density extruded foam, which incidentally is pink. It's mainly used for home insulation and has high compression resistance.
Carving this material on the CNC leaves a nice texture that reflects light similarly to pink felt. It also works well with sanding paper and doesn't shift color too much.

The sheet's dimensions are 1250 x 600 x 50 mm, which allows me to make 2 waveguides. The resulting waveguide has a dimension of 560 x 560 x 48 mm / 22 x 22 x 1.9 inches.
I've made a simple mounting system for the waveguide that uses wood screws and neodymium coin magnets. I've made it like this so that I can adjust the distance of the waveguide from the cabinet, and also for removing the waveguide when needed.

The waveguide sits flush, or can be pushed out by unscrewing the screws on the cabinet. I can also rotate the waveguide by 45 degrees.



Now for the measurements:
All measurements done on spin rig, at 1m distance, 5ms gate, no smoothing. By "sq" I'm referring to the squircle waveguide.
I'm not sure if any shape or size of baffle can flatten the on-axis response of the tweeter relative to off-axis, 20deg onwards. If I'm wrong, please tell me so.
My man, you are wrong again! By making a proper waveguide, you can flatten the on-axis response of the tweeter relative to off-axis. /s
Tweeter:
Tweeter response on-axis with and without sq waveguide:
On a serious note, I never imagined that a larger waveguide would actually improve the on-axis response of the coaxial + horn tweeter, but it definitely does.
Interestingly, the response of the tweeter is only affected on-axis, and once it reaches 20deg the waveguide has no major effect on response.
Tweeter response off-axis 20deg with and without sq-waveguide:
Rotating the sq-waveguide by 45deg doesn't affect the tweeter response in a noticeable way.
Pushing the sq-waveguide out by 1cm has a slight effect on the tweeter response.
Midrange:
Adding the sq-waveguide affects the on-axis midrange response considerably.
Rotating the sq-waveguide by 45deg smooths out the midrange response ranging 800Hz-2kHz, but nothing major.
Pushing the sq-waveguide out by 1cm has similar effect as rotating by 45deg.
Spins:
Tweeter with and without sq-waveguide:


Nice!
The on-axis is better now, but the listening window response is similar to the one without the waveguide. Probably that's why the listening tests I've done didn't sound very different.
Midrange with and without sq-waveguide:


Not what I expected, but also nice. The issue at 2.5kHz is worse now, but the directivity is improved at 1.5kHz, and I can take advantage of this by moving the crossover point under 2kHz.
Distortion seems to allow for a lower crossover point, ranging 1.5-2.0kHz:

And lastly, 360deg spin with and without the sq-waveguide:

It seems that my efforts were not wasted, and with more crossover optimizations and few PEQ filters will give me a good performing system.