Not sure if this will help in an MMA fight, but... just this week my coach was teaching me this combo in Muay Thai where he had me, from just about the edge of kick range, spring forward with a jab - it kind of seemed to me like a swordfighting thing I'd see in a movie, where you spring forward off your rear foot and throw the jab, if that makes sense? Anyway, you spring forward with the jab and close distance that way, it's pretty fast, then you throw a right cross, then something with the left, and then you move back out of punch range quickly. He had me doing a few different things with the left, a body shot or a head hook or even just a weak jab as I moved backwards (for distraction). Again, not sure if it would help any in MMA, and obviously the other guy isn't just going to stand there while you do this, but maybe something similar could work for you?