This should get you in to the MP, and unfortunately you'll have to manually enter it every time to play MP (until they fix it, or if they fix it) but you only have to enter the key like in the box by itself when the window pops up, not the whole login screen thing like I said in the beginning of the post. THAT part is only done once. There you have it, working MP with the annoying case of having to re-enter the key every time until they fix it being saved.
I know this won't fix it for everyone but maybe it'll work for you like it did for me.