Hmm... how about this:

If you queue as the Adventurer in Need, you get a consumable item that increases your XP-gained for one dungeon. This item can be gained once every 60 minutes. For tank mains, this is just another nice bonus, but because it's only once per 60 minutes, if you're always queuing as a tank, you will only get the item once every 2-4 dungeons. Meanwhile, if you're a DPS main and you play tank for one dungeon, you get the bonus item, then you can go back to DPSing for the next dungeon. On top of that, since DPS queues are longer, the 60 minute limit on the item gain is oddly more beneficial to DPS. If you're forced to wait for 40 minutes in a queue then use your item in your dungeon to increase XP, you can then queue tank again right after and get another item. This should increase XP gain on their main class for DPS that queue as tank/healer.

However, I admit that it has plenty of flaws. The one that jumps out at me the most is that it still forces DPS to play something they don't want to just to get better XP. And I think a lot of people would rather just take slightly slower XP gains in exchange for actually playing what they enjoy.