Put bluntly match quality is abysmal. There are far to many leavers ( at least 50% of my games have one or more persons quit the game before 20 minutes), and most lane match ups are very one sided in the player skill department. To many times now have I wanted to comment on item or champion balance only to find no good quality matches to base it off of. The current testing environment makes it very hard to develop an informed opinion on champions, or items because matches are such a landslide.
I would suggest developing some type of ranking system that pools players into three groups. These groups would consist of Good, Average, and Needs Improvement. A combination of hidden MMR comprised of Win/Loss ratio and average Champion Mastery Grade per match could be used to distribute players into pools after X amount of qualifier rounds. Have the qualifier rounds be required every 30 days regardless of tier or the next time someone logs in if they haven't played for over 30 days on the PBE.
To help alleviate que times have Pools draw from one tier lower than they are after X minutes on Good and Average, and allow the Needs Improvement Pool to pull from players one tier up after X minutes.