already think you've got what you need but....

If there's a genuine misunderstanding they'll sort it, as they have access to your chat logs at the time you were banned, and everything you have ever said (and ever done). email them all the details but be prepared to wait 2-5 working days as they get 1000's of emails every day. send an email to support[at]spacetimestudios.com replacing [at] with @.

Good Luck with that...