I'm curious about the tetramic too. I think the original soundfield patents are expired and as I understand it, the software was written specifically for the response of the particular capsule used and the physical arrangement of the four. As for choice of pattern, cardioid capsules are easily available and inexpensive. I'd think they'd be the natural choice, especially since the omni and figure 8 compontents of the cardioid pattern have the same relative sensitivity.
I've never used an ambisonic system and I'm by no stretch of the imagination an ambisonic expert, but I imagine any pattern that falls somewere between omni and figure-8 could work in the array, as long as the weighting of the matrix was to be changed to match. A pattern other than cardioid would need the balance beween the omni and the figure-8 components adjusted (in the software in this case). Patterns to one extreme or the other would be less optimal as they would eat up the available headroom dynamic range if they needed large scaling factors. Using hypo-cards, you'd get more omni component, and would have to scale that down to match the level of the figure-8. Didn't the original ambisonic equations call for scaling the W component by .707? Could that have been to compensate for the extra omni content in the A format using hypo-cardioids?
I may be completely off base here and appreciate clarification by those who know. Tell us more about your interesting mic, Len.