Try taro, maybe ginger, maybe a water spinach like Kang Kong or even watercress. Probably too cold for bananas but they'd look great and might pull some moisture from the soil. Wonder if lotus would work?

maybe cranberries or rice?

Need more information to make a specific recommendation.

What is the soil structure there?
How many square feet do you want for the garden?
How many hours per day do you have direct sunlight?
What specific plants do you want to grow in addition to tomatoes and okra?
How much time and money are you willing to invest?

Having unlimited free water in the desert could provide you with some unique advantages and opportunities.

Since you to want to grow vegetables, you will need to either raise the plants above the water table, lower the water table, or a little of both.

12" or higher raised beds with coarse well draining soil should work quite well IMHO.

I agree with pp about raised beds. My garden is in an area that just gets washed out when it rains but raised beds have worked great for us the past couple of years. I have some 6 inches deep and some 12 inches deep.

The area is about 30 feet long, 15 feet wide. The front area is a bit higher than the back. I don't have a lot of room to build the front up as the soil is already at the level of the sidewalk. The sidewalk goes around our pool so it does need to look nice and soil needs to be contained so as not to escape into the swimming pool.
Soil is heavy clay without any rocks at all except for escapes from the rest of the yard which has been "xeriscaped" but natural soil here has no rocks, not even a pebble. Very fine clay with only the organic material that I've added prior to this spring's planting. I will of course continue adding tons of organic matter. I've added store-bought compost, worm compost and alfalfa pellets so far. I think I used about 1,000 lbs of compost, 360 lbs of alfalfa pellets and about 50 lbs of vermicompost.
Our soil is very alkaline and I have to add frequent iron supplements because of this due to chlorosis symptoms with my peppers, beans and almost everything else that I've grown in my other areas of the yard.
The backside of the garden (lower edge) has a very, very old weathered border of railroad ties that I could build up the soil to which would probably give me about 8 more inches than I'm already at. This would probably level out the garden from the slight hill that it's on right now.
I'm thinking that I may need to have an irrigation expert come look at the huge irrigation gate (big pipe) and see if there is a type of fitting to run a soft hose to and divert water to the front yard. Perhaps I can start a bermuda grass lawn in front. This could solve the problem completely.
French drain plus berm may be a temporary solution. Have a person coming out in about a week or so to dig a hole for a 500 gallon propane tank. Will see about putting the dirt along the back edge as a berm. Then, will get some good garden soil delivered to build up the backside of the garden. Any idea how many cubic yards of soil I should have delivered?

It sounds like a number of raised beds would fit nicely in your space, the taller the better.

I also live in the desert on the same type of clay that you described. I have constructed eleven raised beds in my garden with various soil mixes. The beds that use a high proportion of clay soil tend to drain slowly and retain a huge amount of water because of the tiny soil particle size. The clay here also has very high pH and requires large amounts of acid and sulfur to correct, which exacerbates the problem of high salinity often found in the desert.

Filling your beds with a properly designed soil mixture will solve your drainage and pH issues. Avoid using any of your native clay soil in the mix. Your plants will be much happier.

Buying commercial garden soil mix is a dicey proposition since you don't control what went into it and haven't tested it. It could be worse than your existing soil for a number of reasons.

This thread from the Container Gardening Forum has a great recipe for well draining mixture and includes suggested fertilization products. I think you should give serious consideration to trying Al's mixtures in at least a few of your raised beds.

Here is a link that might be useful: Water Movement and Retention