Dan, wouldn't the other two primaries now be connected in series across the two still-hot primary phases, i.e., in parallel with the still-fully-energized primary? Wouldn't they now each see half of their original line-to-line voltage, and create two 60-volt sources? Of course, there would no longer be a phase difference, but wouldn't there now be 120, 60, 60?
Yep, I was thinking the same thing after I posted. Drop one line side leg of the delta and you will have one winding at full voltage and the other two in series with the same voltage. By eye I had put in 0 for the dropped leg but it will not be 0. It will float in the middle with the secondary load, a voltage divider.
I am thinking possibly you could short one of the secondary windings and the 120 will appear on the other, but IDK. I was actually thinking, why don't I have one hooked up that I can single phase the primary and measure the secondary voltages. Then I would short the 60 volt secondary and see what happens.
Once I could observe the physical reality, backing the math out of it would be easier.