As someone who played WOW and hopped to FFXIV - many of the things that are acceptable and even commonplace in WOW are straight-up against the TOS. For example in WOW it's very common to call out or even just straight-up vote kick a player for messing up one single mechanic in a fight. That doesn't fly in FFXIV. You can't call someone out or blame someone for a botched mechanic or even a wipe. You can ask them if they'd like some advice, but if they say "no" you have to consent to that. You also can't comment on their DPS or rotations, you can't refuse to do your job to spite them either. (So for example you can't refuse to heal a DPS if you think their rotation is bad) Again, you can ask if you can offer advice, but they are free to decline.
WOW shout chats also tend to be very "political" and discuss many "social issues" (at least when I was still playing), that doesn't fly in FFXIV. Things like politics, social issues, and religion are not okay to discuss, even if you are in a private or semi-private chat (like an FC chat) if you make a comment that makes at least one person uncomfortable, they are within their right to report you and a GM may take action against you.
Now, I'm not saying you did any of these things specifically, but I'm trying to give you some examples of how the two games differ to help you understand what might of actually happened. Because, you're right, you probably didn't say anything OVERTLY offensive, but to catch a 20 day ban, which is quite severe, something you said violated the TOS.
I don't think transferring servers is a terrible idea, you're on a very populated one, it would even be beneficial for you to duck out of there before Dawntrail and guarantee yourself a lower queue time elsewhere. However, you may need to examine your behavior and how you are speaking to other people and the topics you are bringing up. Because if you are violating the TOS, even if you didn't intend to, the same problems (except the stalking obviously!) are gonna follow you. Here's a link to the prohibited behaviors in FFXIV.