I think I said the solution in another topic its what Blizzard did. You need to offer a big enough reward to get tanks to queue into dungeons solo not with their friends. You can give them a grab bag that they can earn once a day but it requires you to queue solo. It had about 100 gold in WoW which is like 100k in FFXIV and about a 15% chance at a mount or minion, these mounts/pets were often dropped in old raids/dungeons. So to make it so more tanks want to queue up you offer the random bag that always has 100k gil and a chance at all the primal mounts and dungeon drop minions. When they added the grab bag the dps queue times went from 30-40 min to 10 min.