In the US, the two "unofficially official" RP servers are Balmung and Gilgamesh (see http://ffxiv-roleplayers.com/showthread.php?tid=2632), so nominated by the most active RP-oriented FFXIV website.
However, both servers are perpetually locked for new character creation. I've checked almost daily for a month. I have NEVER seen either server open.
There is a work-around. If you create another character on a different server, wait three days, and then spend $18 to transfer the character, you get into a locked server. Your website says this isn't allowed, but it is commonly done. See http://na.finalfantasyxiv.com/lodest...nsfer_service/ which has the statement "* Characters cannot be transferred to a World which has already reached the limit for character creation."
Therefore, as it stands right now, there is a $18 "RP Tax" in effect for North Americans who want to transfer to servers with an active RP community. I suspect this is a useful secondary income for Square Enix. Check your metrics - what proportion of the North American server transfers are going into Balmung or Gilgamesh?
I believe the reason why Balmung and Gilgamesh are perpetually closed is a bug in your server-closing logic. Role-players tend to congregate at certain locations for conversation - typically the Adventurers' Guild buildings in the major cities. These regions may look "overpopulated," but in fact a large part of the player population is just using chat. In fact, your server closing logic could have other bugs, such as not recognizing various categories of inactive players.
Yes, you could argue that players should nominate another RP server. However, the existing RPers on Balmung and Gilgamesh resist this. They constantly recommend that players pay for transfers, to insure their own servers get as many new RPers as possible (to replace the inevitable attrition of players, or "churn").
As it stands, it is easy to believe that Square Enix is simply enjoying the income from the "RP tax." To dispel this impression, either enforce your own rules about no transfers to closed servers, or update your closed server code to be RP-aware, or both. This will sooner or later force RPers to expand to other servers, as they should, rather than Square Enix profiting from this hidden cost foisted upon a subgroup of players.