Never thought it would happen, but I have an area cleared of bermuda. It's not pretty, but here's what I did.
I started at the edge of the house and worked my way out. This way I'm fighting it one direction. If you don't have a wall, maybe start at a sidewalk. Or start from center and work your way out. The key is getting that buffer, where the edge bermuda has to travel far to get back to your cleared area. Keep making the buffer bigger.
By ugly, I laid down plywood and cardboard. And rocks and boards to hold it down. Any bermuda that poked up was dealt with based on my time. Some I dropped paper shreds over it. Some I plucked with my fingers, some I dug out.
Around my blackberries I used just paper shreds. It formed a paper mache layer but new canes came up just fine. The bermuda didn't come straight up, it travelled under the paper til it found a void.
So the last month I'm down to maybe 3 or 4 bermuda coming up every week around my blackberries. The roots are losing their energy. Im.winning!
I have had similar results with putting down large sheets of rubber roofing material and leaving it for a year or more. You're right, it's ugly. But much more beautiful to my eyes than the $^#(& grass! After everything is thoroughly dead, I remove the rubber and pile on the wood chips. The grass does try to encroach from the edges if you don't start at a wall or something like you did. Now after I clear an area, I leave a "DMZ" of black rubber 5 or 6 ft across all the way around. In a couple places I am trying a border of comfrey to see if that stops the invasion, and I have high hopes for it. I will probably try hostas in an area as well.
Congrats on the win
"People may doubt what you say, but they will believe what you do."
Besides the ugly, I did get significant ant populations under the plywood. It was good and bad. Hand pulling bermuda was risky but the super aeration from them made it easier to pull more of the plant.
Sometimes the answer is nothing
Getting married means "We're in love, so let's tell the police!" - and invite this tiny ad to the wedding: