
This happens on actual hardware:

It's clear that the hardware has an easier time driving the neutral electrode. It's a bit difficult to see because I used the cheapest multimeter on the planet to perform these measurements, but the full degrees of freedom are there.
I hypothesize the hardware does a modified version of the ab-transform in which the poles are not at a 120° angle. The first image was generated with the usual ab-transform, what happens if we use a modified ab transform with the poles at an angle of 150° relative to neutral?

That looks a lot like the measurements from the 220 ohm case. let's call this transform the hardware transform. Now all we have to do is calculate the inverse of this transformation matrix, multiply that with the waveform before we send it to the box, and the box will output a sweet, sweet balanced waveform. One-parameter calibration, no hardware modifications necessary. I will document the full details later.
I think we can do the same in hardware by simply adding a resistor to the neutral output. I tried adding a potmeter, but it didn't take long before it released it's magic smoke...
Edit: here is a measurement after calibration:

There remains a small L/R calibration issue, but otherwise the box generates the waveforms I expect.



