I've got rid of a few acres of Kikyu grass. (I'm not sure of the spelling) but it sounds like your Bermuda grass in habit - deep long runners for roots. Repeated spraying is fairly sucessful. Mulching works to a degree but sends some roots further down. The easiest method was thick black plastic over patches of grass under the hot sun. I move the plastic on after about 6 weeks and plant the area up with local plants. I have to time it all fairly carefully so as to plant at the ideal time but plastic, then mulch, then planting seems to work quite well. I always have to pull up some resistant runners for a time. We don't have lawn either just native grass mostly in clumps. We still have three paddocks of introduced pasture grass to reclaim outside the house garden. 2 acres down 2 to go or there-abouts. Joy