I flew alaska air a couple months ago, and all I did was I had one carry on suitcase, and had my scooter all put together, but my scs was loose. I just rode it through security(took my bars off to get it through the scanner, and then just rode it the rest of the way to my gate, then took the bars off again to fit everything in the overhead compartment.
So, if I were you just bring one carry on bag, and then you can just do what I did and bring your scooter through with it all put together, but make it easy to break down.