Experimental Garden. Will Anything Grow?

[Bock-Bock-Bagock]

TLDR Version: Hard clay and rock ground. Gets super wet when it rains a lot. Does drain eventually though. Gets full sun in most of the area. What can I Grow here? If I can't get veggies going I might just make a fruit tree orchard next year.

Full Story:
I have this space I want to try to grow something in. It's 60% rocks held together by clay. My dad tilled the area to loosen it all up. As you can see, it gets flooded when it rains. I'm in central Tennessee. So you know the rains we've had in the areas the last few days.
It seems people do a lot of corn, which is something I am trying in the back area. I put in some potatoes closer to the front in the picture where you see the trenches. I'm kind of worried they are just going to drown now. I did put in trenches for drainage, which it is doing now. But so much rain is dropping. Which should be less of an issue in the summer.
I put in carrots, radishes, broccoli, lettuce, and cabbage. All of which I read can handle clay soil. So far none of them have sprouted a thing. It's been about 3 weeks.
I wanted to try sunflowers mixed in with the corn. I wanted to do cucumbers where you see the cattle panels. Under the cucumbers, I wanted to get some shade plants going. Maybe broccoli and lettuce or herbs. Closer to the raised beds I wanted to try different peppers.
The previous years I've used raised beds, but soil is expensive and I can only do so many a year. Then the raised beds fall apart. This year I am trying to figure out what can grow well in the soil and lean into those plants. If I can't get a good harvest from this I may just start planting fruit trees in the area.
Any suggestions?

 

[WingItRanch]

We have a clay base here in East Texas with some sand. Didn't have any luck with root vegetables (no carrots, onions, potatoes) but for some reason green beans love it. Have also had luck with summer squash and cucumbers. Still working on the perfect garden. Start composting your chicken litter. Eventually you'll build up a better garden base. Maybe look into a French drain around the garden to get the standing water out.

 

[Bock-Bock-Bagock]

We have a clay base here in East Texas with some sand. Didn't have any luck with root vegetables (no carrots, onions, potatoes) but for some reason green beans love it. Have also had luck with summer squash and cucumbers. Still working on the perfect garden. Start composting your chicken litter. Eventually you'll build up a better garden base. Maybe look into a French drain around the garden to get the standing water out.

Potatoes do well here. My great grandfather had a potatoe field that my dad owns now. There's been decades of potatoes. So I'm hoping I can get them going up on my place too.
I tried beans in my raised bed and had no luck previously. But maybe I'll try them this year in the clay. See how they do.

 

[CatInTheHenHouse]

Try straw bales instead of raised beds?

Fair warning, I haven’t tried it myself.

 

[Bock-Bock-Bagock]

Try straw bales instead of raised beds?

Fair warning, I haven’t tried it myself.

It's worth a shot to pick up a few bails of straw and see if it works. Only concern would be that most commercial operations use Roundup in production. I'd really like to avoid that if possible.
Perhaps I can source some localy grown. Before I moved on this propety my grandparents would let a local guy grow whatever straw crop and harvest it. They didn't do anything other than let it grow naturally then harvest.
Would actually make a better option than growbags too, as it is an organic medium that will break down and get spread throughout the area.
Thanks for that.