Bermuda irradiation before St. Augustine sod

I have read MANY posts about the life-long battle between man and Bermuda and learned much but I have a more specific question. I just moved into a new house in Houston, TX (zone 9) that did not have sod in the back. In the meantime Bermuda grass has moved in and set up shop. In preparation for my St. Augustine sod I pulled all of the weeds and went to work on the Bermuda with a hoe and an attitude. I have basically turned over all of the soil that has been infected by this devil grass, pulled out all of the roots and stems that I could find, and have started laying the St. Augustine down on the remains. After reading posts here I now see that I may have only made matters worse by digging and that the Bermuda will likely shrug at my attack and grow up through the St. Augustine. At my stage of the game is there anything I can do to preempt the Bermuda from growing in my St. Augustine?