Starting an acre market garden on coastal bermuda

It has a slight South East slope.
Coastal Bermuda growing throughout. This has been a leaf dump site for 20 years.
I want to have a garden producing by the first month of April.
To knock back the grass I we are going to rent a moldboard plow and flip it to expose the roots, then rake it really good! Wait two weeks and do it again. Build slightly mounded mulched beds 5' beds with 4' path with drip lines running from west to east. Irrigation will need to be put in under the road. Then start popping transplants into.
What are other methods for slowing this bermuda?

If that soil is compacted enough to want to till it and make beds like that, go ahead, but you will only make the bermuda come back worse than ever. Tilling, beds, or no, you need sheetmulch. You need to cover the whole thing in paper and cardboard. Especially the planting beds. Do it a few weeks before transplanting, right on top of your irrigation, and then come back and punch holes through and transplant into it. The bermuda will come out of the holes you have punched and anywhere else it can, but you have still given your plants a head start and they should make a crop anyway. I gardened in bermuda for years this way in South GA. For direct seeded stuff....good luck. I had some success tucking in corn, sunflower, and squash into the gaps in the mulch after cauliflower, broccoli, etc. got clipped off, or after white potatoes got dug up. Carrots and such like can work because they start growing well in advance of the bermuda, which is heat loving and frost tender. Just make your beds for those things soon and plant them early.

Bermuda grass dies back in the winter so how effective would it be to smother it? The plants are dry and not using sunlight at this point anyway. I think it would be better to pull as much of it out of the garden before it wakes up in the spring. I know this won't get all of it but it would be a huge head start for the helping me be able to manipulate the surface to better hold water throughout the summer.

With a moldboard plow, flip it to let it rot and breakdown on itself, and if I took it off at this point I would be taking away the top soil.
So next disc it to break it up to rake much of the Bermuda out.
We would shape the beds to slow down water flow.
Our summers are very dry so it would be set up to have drip irrigation.

Perhaps I'm coming from a perspective that seeks to minimize tillage for other reasons (soil compaction, soil food web issues, etc.), but I think you will be disappointed with how much the bermuda will come back. And I hope you do not have nutsedge in there with it.....if anything that is even worse. What I'm doing right now is sheetmulching my garden in sections, keeping cardboard on a section for an entire year or even two to try to smother it out.

Thank you for your concerns and input.
With how the field is and in the time frame I need it, I still think tillage is going to be beneficial. Right now it's a Bermuda monoculture. After we break it up and shape the bed so that water flow is conserved (can't do this with without tilling and very important) We are going to mulch with straw and wine cap mushroom inoculate. The mushroom forms a smothering mat as well as produces tasty edibles and encourages soil life. With compost placed where I put my transplants, underneath the mulch the soil life is going to thrive. If tilling is done with the perfect amount of moisture compaction is not an issue, and even if it is I plan on being no till after breaking it up this first time, and from then on it will be covered and be productive for a poly culture of vegetables.
For my first garden I defeated the Bermuda within two years while producing veggies with this method.
I've also gardened an area that had been sheet mulched with cardboard, the bermuda runners found the cardboard to be a habitat, it probably should have been re smothered but I really didn't like the cardboard. When it was laid the tape a stickers were still on it so I felt like I was growing in trash so I cleaned it out so I could mound and raise beds. This was in a heavy clay that needed this lift keep the plants from being flooded. This area had nut grass, oh what a pain that stuff is!
When you sheet mulch do you leave to cardboard for good and just keep adding more? How do you get to the soil? How do you shape garden beds?

When I was heavy into marketing I didn't have the time to deal with tape, etc. and so like you ended up gardening "in trash". Since them I've de-taped every piece of cardboard as it comes into the garden. Sounds like you are not describing tillage so much as earthworks.....a one-time disturbance event to configure the landscape for productivity. Have you done the mushrooms in the mulch before? I'm amazed that they can be productive even of mycelium, much less mushrooms, with the hot and sometimes dry summers. Especially with drip irrigation.....maybe if you were sprinkling the whole area they'd have a chance. But that's just my hunch. I've only ever picked wild mushrooms (which ordinarily show up only after a good rain), never grown them except a few shiitake on logs. So you are saying that tillage, beds, and two years of dense plantings subdued bermuda? Either you were doing something very special (voodoo maybe?) or you had some pretty lame bermuda!!
When I gardened at scale, for market, I would till and make beds, and then either plant first and mulch soon after (often with small paper or newspaper) or mulch first and transplant through. Then I had to mulch every year. Since then when I've gardened on a smaller, home-use scale, I've cardboarded a whole area and then piled compost, manure, and clean soil from elsewhere in beds on top of it. This method sometimes would subdue the bermuda for a couple of years and then I'd be papering around stuff again, or else succeeding the whole area to orchard/food forest.

I live in the southwestern part of Texas where we have some major issues with exotic grasses including Bermuda, KR Bluestem and much more.

We are in the 25+ inch rainfall zone. In the past 5 years of extensive drought we have received no more than 18.7 inches in one year. In fact in 2011 we received 4.9 inches on our ranch. My point is Bermuda grass can and will survive anything. We use a very similar method of gardening: we built 4 ft wide raised beds by hand (40+ ft long) with about a 3 ft walking path. Like I said all dug by hand and during that process we literally sifted through every pile of dirt and removed Bermuda grass roots. 2 rows of drip pipe top each row with anywhere from 4 to 8 inches of wheat straw mulch. GUESS WHAT? Regardless of our extensive efforts the Bermuda grass was back strong withing one year. We fought it as it came up in various places, but it won the battle.

Other methods we have found useful: during the Fall months we cover crop heavily infested areas with a mix of wheat, oats, clover, turnips, and winter peas. This seems to choke it out during the spring when the Bermuda grass comes out of dormancy. Doesn't fully solve the issue, but alleviates the problem.

My best advice is to keep your garden covered in something. Whether it is plants or mulch. The best way to fight Bermuda is to out compete it on the phototrophic level.

Plowing won't resolve the issue, and neither will mulching heavily with cardboard and straw (we tried sheet mulching too). It will just take a little longer to come back. Once you have it there is simply no getting rid of it. Do your best to protect your garden borders. Perhaps a chicken run around the entire border to keep it beat down. Or shade it out along the borders with dense trees and bushes. Bermuda doesn't like to be shaded! In fact you will not find it growing in heavily shaded areas.

Just some ideas. I hope they help. Don't resort to chemicals because they don't solve the long term issue either (also learned from experience long ago).