Well, that was a tricky ride :)
I still have not got any clue how this all worked. Finally I came to the solution of a completion spreadsheet: queue character names and mark them with a “+” if typing “conscript” in the collections tab showed an appearance in every slot.
Mark you, it has to be done and checked character-by-character. For example, earning a cloak for my dwarf shaman does not show for my night elf and draenei hunters. But once the draenei Kalaari earned it, it immediately clicked in for both hunters and – ta-dam – also as a leather cloak for all leather Hordies! This is the most mysterious collection gathering I’ve ever had in WoW.
Alliance Transmog Sets:
Horde Transmog Sets
That done, now we’re going for pet, toy and upgrades. Most weird, most weird event!