I'd love to have this, in my case, to move the party list between healing and damage roles. For a workaround in your case though, take a look if there is a keybind to toggling the particular elements you want hidden or not. You could also make macro that toggles the visibility of various hud elements. Sadly the moving of them is not as easy matter.

http://na.finalfantasyxiv.com/lodest.../text_command/

The command you're looking for is /hud in category "Other".