I'd like to be able to see the arena ratings for all my characters at a glance (2s, 3s, and RBGs).

A slash-delimited list would probably work just fine. Something like 1550 / 1260 / 1650 or with their labels like 2s: 1550 / 3s: 1260 / RBGs: 1650 would be sufficient.

I've looked for other addons that can do this, but there don't seem to be any that will show me arena ratings of all my characters.

Could probably use GetPersonalRatedInfo API call, but having never written a WoW addon myself I'll have to defer to the experts.

Currently RBG ranking is tracked. You can find it by hovering on character names. 2v2 and 3v3 will be added in next alpha version.