Seeing as they made "A" the start button once you are in the game, then yes they definitely could have made a button config. That means they had access to the controls. I think the reason why they didn't allow for it because of something to do with the triggers and bumpers. I bet if you changed the button or something it would make both sides the same thing, which even though it sounds ridiculous I could totally picture happening. On PSX MKT, I got very use to having Block and Run both on the right side, but then I got a PSX arcade stick.
If you can open it up and reset the button layout manually you could have something reasonable on the 6 button face. What I would do is on the top BL, HP, HK and on the bottom Run, LP, LK. If that is possible and you can still change button layout in game for other games then you should be good to go.