That means it's not open

The only thing that is 100% correct with whether a server is open for new characters is the game itself. If it lets you create, it's open. If it doesn't, it's not.
The website (or other 3rd party websites) aren't live, they're showing the status at that point in time. With the
official page there's a time at the top to show when that page was updated as well as it starts by saying "This information will be updated at the following intervals:". The server constantly opens/closes, the webpage does not constantly update to match it.
Sorry I have no experience with the world transfer tool myself, but from make sure you have the right data centre selected (if it gives you that option?) as well as I understand it actually asks you for the source server first, not the destination? Also your character has to meet all the requirements (I believe it tells you if it doesn't though?). Sorry bit vague on this part, but hope it's of some help!
Edit: Just saw another thread where someone can't do a paid world transfer to a full server so maybe they've stopped allowing paid transfers to override the closed server.