I hate to be a downer but manually removing every little piece of Bermudagrass is really the only way to get rid of it. A couple feet of new soil won't discourage it and may encourage new rampant growth.
Chemicals don't work all that well either. Here's an article about it from the University of California's Integrated Pest Management program. Solarization could work for you but you would have to give up your vegetable garden in that area this year. The geotextile fabrics don't work - the holes are just big enough for the shoots to come through. Unless you are willing to track down every little runner, even if its going through a plant, you will lose this battle.
http://ipm.ucanr.edu/PMG/PESTN...
