You'll probably be happier wtih 480p then 960i. 960i is just a silly way of upconverting 480p.
Anyway, if that game supports 1080i, then something is wrong as your TV is in 480p mode.
You are correct that the Cox tuner is going to use your single component HD input. If you have DVI or FireWire you could possibly use that, however, I believe those ports were part of the Mitsubishi HDTV Tuner, which as you said you don't have.
I don't know if the Cox tuner will let you piggy back the XBOX off of it. It seems possible but I don't think I'ev seen a box that lets you do that. You could consider getting a manual component switch box to switch between the two. But you'll need to be happier with your XBOX HDTV apperance before that is worth it to you.
If you do get your XBOX to output 1080i successfully, your TV won't let you change the mode at that point. 1080i is 1080i and that's it, so there is no, switching from 480p to 1080i and back if your XBOX is outputting 1080i.
![beer :beer:](https://forums.xboxscene.org/Smileys/xs/beer.gif)