Dragon Age Origins Ultimate Edition on XBOX 360

Hi.
I've bought and played DAO and DAII for PC, and finished playing through DAI on my X1 a few months ago. I then felt like I wanted to play it on my X360, so I recently bought DAII for my X360, thinking that I could just access the DA Keep to continue or even create a origin from DAO. But I realized I couldn't. Annoyed, I tried to buy DAO so that I could play DAII. Now, my question is, to I have to buy a brand new DAO Ultimate, since I've already bought for my PC, or do I need to get a brand new one? It would have just been easier if the Keep could work for DAII, but I guess that's not possible.

Thankful for quick response. 🙂