Since all of the threads on this topic appear to have trailed off without an actual conclusion, I can confirm that a standard crossover cable (pinout 12345678->36145278) did work to power this from an Arista 710P-16P (on either a 802.3at or 802.3bt port).
Zero activity with a standard straight-through patch cable, worked immediately with a crossover.
A slight faff to have to manufacture one of those, but if that's the worst problem these units have I'll live with it.