What about this:
You queue up for a dungeon as DPS. It's a bad day and there are barely any tanks online. You would usually have to wait for hours in the queue.
At x minutes (where x is a very LARGE number), a pop up appears: "It seems we are short on tanks! Would you like to try with an AI tank? Click yes to accept!". It is optional.
You say "yes". You and 3 others who also said "yes" get grouped up into a dungeon, where the four of you will follow a software-controlled, well geared up tank. He knows the dungeon tactics but is not invincible. You'll healer will have to keep him up, and you'll have to follow usual tactics too.
If you say "no", you retain your spot at the front of the queue until a real tank arrives.
Thoughts? Yes, I know I'm probably not the first to suggest this.