Have you guys considered hiring/consulting with psychologists on player behavior? I'm sure you could probably find some in academia that would be interested in helping you look at the issue from a different perspective. Just an idea.
I would really like you to consider short term/temporary bans from things like just ranked queues. Say someone is "auto detected" by a new system instead of jumping to a multi-day ban immediately, issue some kind of warning message and disable their ability to Queue into Summoner's Rift for a day then next maybe 3 days. It would be good if you included in these ban messages more than just how naughty these players are being.
Including in these messages something like statistics on players that keep positive attitude increasing rank and winning more games (because they are out there many of us have seen them). Encouragement to reform could also be effective is what I am saying.
Thank you very much for addressing this directly, just knowing you are working on this is better than nothing. I think the community will be forgiving as long as you are trying to fix the problem even if there are mistakes made while getting to the most balanced place possible in this respect.