While bonus rewards for playing as a tank or healer sounds good on paper, in practice, the DPS still queue as DPS and the tanks and healers just get shiny new awards to go along with their faster queue times... so really, DPS just get even more shafted than they already were.

The only feasible and logical answer to this particular conundrum would be to restructure the current group setup to allow for a larger number of DPS in each dungeon run.

Considering all the balancing this would entail... it's certainly not a quick fix, but is also unfortunately the only fix with a dependable outcome.