I assure you that no matter how it's implented, passwords are WAY easier. Reasons why:
1. You can just tell all your friends the password ONCE, and use the same one each time. Inviting each individual each time is such a hassle.
2. If your friend decides he doesn't want to battle ATM when you send him an invite, then he decides to battle again later, you'd have to do invite them again, AND they would have to PM you, and if it's in the middle of a mp game, you might forget to check their PM. If you guys kept a consistent password, they could just enter the password, and BAM. Easy.
Of course, it would take a couple sessions until you all memorized the password. Telling everyone to write it down solves any 'what?' issues. As to spreading it, do a forum PM, but send it to all of them at once. Good thing you can do that.
Now that I think about it, having a forum PM would also have a place where they have it if they forget to write it down.
Anyways, I'd go with what Echo said. Personally, I would make sure the 'CREATE ROOM' button is nice, big, and most importantly, obvious. That way people will, well, notice it instead of spamming the chat with 'why can't people see my room?'(then it disappears when you press it. Maybe have it where the Ready and Start buttons are, then have it disappear when you press it, and have the Ready and Start buttons take their rightful places). So yeah, just a big button, and a two option drop down menu (password/open to all), with a dialog box thing that only appears if you have 'password' selected.