The move bit sounded good to me! Cover first of course.
They cant continue to hit whats not there.
Run out on an angle, make them follow and catch them comming.

Someone good in close can bring your guard up or down while launching combos; in this case move out to the side and throw straight controlling shots on them so they have to turn towards you to start over again; but have to turn into your shots at the same time.

Or You could glue to their lead arm push it in and stick with it controlling them as you go out that same way ,away from their other arm fast and throw down on them hard as they turn to face you.

OR you could feel their shot hit you ,follow it back in ,go in further to choke that side of them off and throw the uppercut in there or short hook if their arm drops (do both!launch your own combo) just watch that other arm of theirs, cover its path with your inside arms uppercut as your other arm and body crush controlls their other one.