Appealing via the email provided is probably a waste of time so I'd just wait for a response from BadBear, but using an alt account to post anywhere outside of Meta will likely be considered ban evasion.
I think it is actually pretty rare that BadBear actually responds to these kinds of threads. It has been said that the actions by the moderators tend to be anon to prevent them from being harassed from people they have taken action against.
If you look at the post history then you can see that most of his posts are what I think should be considered to be spam. He also seems to have a very high post count when compared to the fact that he has a paid signature would lead me to say that he was signature spamming and was banned as a result.