I don't think he was muling, he was looking for something since the person he wanted to trade with wanted something overly specific.
Just rejoin the game slowly, don't do switch after switch. Make sure you sure you are in the game for at least 3 minutes per char and you won't get banned.
Maybe start writing down what items you have where or have specific chars hold only armors, other chars only weapons, yet another holding just helms, ect.
If you are temp banned, don't keep checking, that will only prolong the length of the ban.
In case you do have something important you still want to say and you know the recipient's char or accountname, you can go on open battle.net and message from there. You will need a single player char(can be unplayed level 1) to enter the chat area. Then you can message from there to closed battle.net
This also comes in handy when you are busy muling a boatload of expensive items and you get a ban. Hope one of your friends is online to see your plea to pick up your items in game // pass
here's an easier solution: why not name the mules after the items they carry? for example: IGotBelts. It may take a little time to perm and organize at first. But in the long run it will save you countless realm downs while looking for an itemwell thats exactly what happened. I was trying to find a Anarch belt, but forgot where I put it...
Guess I need to make a spread sheet now...