Converting large area of grass to garden

We are newly living on a property in Northwest WA state, with goals to grow as much of our food as possible. Last November we used a sod cutter to strip/then flipped about 3500 sq ft of lawn. We are noticing grass starting to sprout from the surface of the (flipped) sod. Our plan has been to plant a mix of daikon radish and mustard cover crop over most of this area for this coming growing season to start breaking up the sod and improve soil quality and drainage. From an organic matter (and labor) perspective, we'd rather leave the flipped sod in place. However, we're concerned about the grass starting to sprout from the root mat. And we also don't know how well our planned cover crop will germinate/establish from broadcast seeding onto the root mat.

It's such a large area that covering it with cardboard would be a huge project (plus I'm not crazy about using cardboard in areas where we'll be growing food since I assume there must be some residue from the glues). Any suggestions? Would it be safest to just pile up the sod, let it break down, and then put it back in the garden? If we plant our cover crop soon, might it be able to get established enough to outcompete the grass trying to re-grow from the bottom? Thanks in advance.

Covering it with a large tarpaulin is an easy option if you have one available. In my climate it would start to grow back before the cover crop managed to shade it out, so I would try to ensure its dead before planting.

We bought our property 1.5 years ago and found ourselves facing your predicament as well. We've tried a few things:

1. Raking/mowing down the grass as far as we could, then covering with a tarp for a few months. That only worked slightly. The grass roots didn't die, and they were thatched like crazy! We felt like we'd wasted our time with that.
2. Double digging. It worked okay, I guess, but grass still popped up. (And crabgrass crept in. Oh how I despise crabgrass!)
3. Digging as deeply as we could with a shovel and throwing the contents onto a hardware-cloth sifting table my hubbie built. Then as a family, we all pushed around the root clods until all the dirt was back in the ground. The roots got burned. That was, by far, the most effective method for us. But boy howdy, that's hard work!!
4. Our new favorite method is to completely dig out as much of the dirt (dead sand, absolutely no tilth) and dump it with the grass into a large pile at the back of the property to just decompose on its own. We fluff up the remaining soil and add compost back in until the soil level is about back to where it originally started. The old grass is composting gradually on its own in those piles. We'll use it when it's composted, or we'll sift it out if necessary. This method seems to be less labor-intensive than sifting it out right away.
5. We're hoping to do more raised bed gardening in the future, but with construction supplies being so expensive, we'll continue in-ground beds for the foreseeable future.

If you are able to use a sod cutter again, I'd suggest removing it completely from the garden area and letting it compost in a separate place. If your grass roots are like mine, they're indestructible!

I'm wondering what exactly you're planning to replace the grass with?
That would really establish what method to go with.
Also, what is the planting strategy and phasing based on the design?

This will be for primarily vegetable beds, though we will also have fruits like blueberries, raspberries, strawberries, kiwi vine, etc. Potentially some grain, too, since it will be a large area. But vegetable beds for the majority of the area. We are planning to bring in a garden bed soil mix for a portion of the area so we can have some garden this coming year. But for about 2/3 of the space, our plan for this year was to just cover crop and try to enrich the soil (and potentially give time for the sod to rot) for future years.

I would put cardboard over it if you have some available, layer it nice and thick, and place some rocks over it incase of wind. It should help kill the roots. Then build your raised beds on the cardboard.

I would just hack away at it one piece at a time. Maybe put in some chickens in a rotational system, let them pull the grass out for you and work your soil improvements into the soil.
Im not sure what your climate is like, but I'd plan it in phases.
So let the chickens remove all undesirable green things and make some fertile deposits, then go over that area with your cover crop/ soil improving mix. Make sure that you have enough rotational paddocks to move the chickens through in a 3 month cycle. Once the cover has matured (I think deacon radish is like 3 months) send the chickens back into that paddock to completely destroy it, eat it, scratch it into the soil, and poop it out. repeat cycle or broadcast seed and cover with your imported garden soil. Its likely that you'll have food soon after that and much less of an issue with your grass.
To start off with, I would always cover bare soil, even if its turned sod, with some kind of mulch. Either living or dead.
You might also consider other animals. I don't have much experience with them.

I have tried flipping sod. I have tried cardboard and mulch. I have tried rotovating.

IN my circumstances rotovating is a clear winner, followed up by top dressing with a well rotted mulch. I rotovated twice, about 2 weeks apart, and had no grass attempting to regrow. I was able to plant almost immediately and weeding was easy - a quick strike with the hoe.

I do still use plenty of mulch, but I will start beds with the rotovating from now on.