Go to run, type command. When a dos like window appears, type ipconfig /release . Then after that process finishes, type ipconfig /renew. This should give you a new ip address.
I don't think it really matters how many games you go to, just how fast you go to them. When you leave a game, wait like 10 seconds then join another one. I know it sounds annoying, but it's better than waiting for an hour for your ban to go away.
If you've got a static IP address from your ISP, the only way you can change it is to call them and get a different one.
There's two things I've seen. Realm down, and Unable to connect.
I've avoided both of these by basically making sure I'm in the game for at least 60 seconds. I've successfully muled/mf'd this way, switching to all 16 characters (2 accts x 8 chars). It's after you exit a game within 60 seconds a few times (not sure of the number) that you get either one of the two messages, from what I can tell.