I don't really understand the zealous negativity here. Yes, in the normal Tribunal topic where the banned baddie complains about how they got banned for carrying, it's completely appropriate to call BS.
When the guy comes right out and admits that he deserved his ban, apologizes for his behavior, and accepts that he needs to step up - that's not a good time to act like a failboat. Whether or not he's serious, whether or not he can do it, that is the time to be ENCOURAGING, to try to manage that last little push to help the guy reform fully.
/cynical and pragmatic optimism
But yeah, hope that works out for you OP. I know how rough it can be to deal with a long day of idiots/work/college/etc and come home to trolls in Ranked, but if nothing else hold fast to the data about how people who don't rage win more games, and how teams that don't dissolve into fighting win more often; if all else fails and you really want to tell the 0/14 guy what you think, just remember that and it might help stay your hand. None of us WANT to see you banned, and I hate having to punish so many cases. Would much rather just pardon everyone, but I can't do that unless the case actually deserves a pardon.