This recently seen display, although not a bright one, highlights an important issue. There is the Moilanen arc but no plate arcs. "Not the slightest hint for circumzenith arc or sundogs. Absolutely nothing", writes Bertram Radelow, who photographed the display in Davos, Swizerland (air temp. -5°C, sun elevation 9°).
Thus, the crystal wedge angle that makes the Moilanen arc does not seem to occur in plate crystals. Column oriented crystals seem to also be out of question, because in simulations for one thing this orientation would make also lower Moilanen arc, which has not been observed yet. And if we assume that some of the columns or plates take Parry orientation, it makes sense to conclude that Parry crystals are neither the answer.
So, it feels like Moilanen arc crystal makes no other halos at all, and finding the crystals from crystal samples should be easy. But we have looked at many samples already and there has never been anything peculiar occuring in great enought numbers to name as a suspect. It is also interesting that Moilanen arc has not been seen alone yet, which could imply that its crystal after all makes other halos.
It is mysterious, but one day somebody is bound to take those desicive photos. Displays that have common halos only from one crystal orientation (such as here) are of course the best ones to look for the crystal.