So League is introducing a seperate MMR and queue for each role in competitive which I think would be a pretty good idea for Overwatch. What if you had to pick a role (DPS, Tank, Healer) before queueing and were found a match based on that?
I think right away DPS mains will notice longer queue times, but it will also ensure they get matched with tank mains and healer mains of similar SR which I think would be well worth it. Instaqueues for tanks and healers would also be a fair incentive for them imo.
This might discourage off-meta non 2-2-2 comps, but I think it should be fine so long as you're allowed to switch comp up once your match is found -- something to discuss with the team, probably. I think mechanically the game modes and heroes are balanced super hard around 222 though and the Serious Game Mode should encourage good matches.