I own an AI and it is definitely a ton of fun. I think the short answer to your question is no, you won't want to try to upgrade to the AI sail rig.
A couple of things to consider: The Aka support cross bars mount 5 feet apart front to back. I am pretty sure they would interfere with seating. The mounting holes for the Aka supports are 15 3/4 inches on center for the front and 21 1/4 on center for the rear. I believe you would have to fashion mounting plated to adapt them to the gunnels on the Oasis. Also, the front Aka support includes the mast support which hangs down enough that you would probably need to cut the cockpit floor to give it clearance.
Actually, the centerboard is important, not for stability, but to keep the boat from drifting sideways on all but a down wind run. On a beam reach the boat slides sideways almost as fast as it moves forward without the centerboard.
Last, but perhaps not least, the upgrade kit costs about $1,600 plus tax and shipping here in the US. Bottom line: If you want the AI set-up, sell the Oasis and buy an AI - you'll be happier in the long run.
OR - do as Stobbo suggests - sounds like a good alternative.
Sorry for the "pretty sure" and "I believe", but I don't have an Oasis here to check and this is after all just my opinion