Sorry about the multiple messages but these are just popping into my head randomly this morning:
3 - Because the Power Analyzer is showing the voltage waveform for the third phase the idea of using the third phase wire and the neutral wire as an independent feed for the DC voltage could work if the DC source is connected in the third phase on the third phase side of the transformer. There is still the issue that a DC power supply will try to regulate the AC, thus the AC voltage shown by the analyzer would be greatly distorted.
4 - Typical front ends of AC to DC or regulated AC are diodes bridges steering both the plus & minus polarities to the same TRIAC. If this were the case then the currents would be equal but the power measured would be the AC & DC power added together.
5 - In #3 if there was a load at the control box end of the AC plus DC in the third phase wire then there would be AC current, which there is not. Thus this method does not seem likely either.
