This idea isn't perfect, but I'm just throwing the idea out there.
Why not allow players to queue for the lane they want to play for Rank Games? Similar to WoW dungeon instance queue, player can choose multiple role they want to play.
So maybe I want to play either Mid or Support. A box pops up and I click on the Mid Lane Role and Support Role. Then the game come up w/ a team that will fulfill the role I want and covers the other roles in the game. Top/Jungle/Mid/Support/ADC. This will probably cause the game like rank queue time to last few minutes, but long as the queue time isn't too long. I don't think most player would mind waiting few more minutes. Least they will play the role they want, with a players in team that playing the role they want themselves. It should lower the amount of troll games, less likely hood of queue dodge, and people just happy with the game itself.
This isn't a perfect fix and I am overlooking the fact that some role isn't just popular as others. Like not many people I know likes playing support, so the queue might become insanely long for some people. And other problems this might cause. I think this is a fix for solo/duo rank queues. But it's just an idea, throwing it out there. I'll let you guys debate it out.
I think someone already made a similar post on this before, I don't remember.