Honestly, I don't think there's reason to push people to play healer/tank. What's the point of having them do it and perform badly?

Tanking and healing is a lot more demanding than dpsing; so if you are not into it, you are probably messing up the run for another 3/7 people

A solution, in my opinion, would be have players not queue as DPS. Remove the daily roulette rewards if you go as a DPS, nerf dungeon exp for them and buff quest/FATE exp so they go do something else