Position based matchmaking. Done.
All that needs to be done is based on what roles you select, it will then start a selection process to determine who you will face off. Now I'm not an expert. Not even close. But I know there is some algorithms in place already to decide who gets what role, and who gets auto-filled, etc. Why not add a parameter for "MMR" on an individual level?
I'm fairly confident, that if the trade off is say, 30 seconds extra on the timer to get a lobby built; most players would be ok with a fairer matchup in exchange for 30 seconds [or whatever the timer ends up being].
I believe communication is key for the success of the game. So let me know what you all think, and if a Rioter who happens to know roughly 1. If it's possible. and 2. If it would end up being say, 10 minute timers as opposed to the 2-3 minute timers presently.