To self-publish a game to the Xbox 360 Xbox Live Indie Games section XNA is your only option. Licensed developers who publish either full retail games or Xbox Live Arcade games have more options but those are developers who either have a publisher working with them or Microsoft is working with them as a publisher, which I would assume is not the case for you.
As a side note, it's still the solution for 360 indie publishing, but XNA is not being actively developed any more and does not target new Windows store applications for Windows 8 or Windows 8.1. As such it works for 360 Indie games and Windows desktop games, but you you'll have to port your game to move it to modern windows platforms and there is currently no plans to support XNA on other platforms moving forward.