I know this is older, but I also live in Oklahoma (northeastern OK, near Tulsa)..
You're wanting to retain the cooling properties of the earth, but water is an issue here due to the soil. That's why we don't have basements and stuff like that, typically.
What if you instead did earthbag, rammed earth, earthship tire walls, etc... Providing thermal mass... And then set your greenhouse on top of that.. Building up, but taking advantage of the cooling properties of the earth.
You could also take the angles of the sun into consideration and build shaded area into it.. So that the shaded area (one side of the greenhouse) doesn't absorb the sunlight from the summer sun, but allows full sun in during the winter.
Then you can also run some cooling tubes through your greenhouse, earthship style.. And add fans and windows up at the top to suck out hot air during the summer, but keep it during the winter.
Hope that made sense. Just an idea. I've been thinking about making a greenhouse for some things that don't grow around here..
I'd also put in some water somewhere. Some people use tanks, some use barrels. Also helps stabilize temperatures and moisture in the air. You can rig some gutters or roof run off to collect and take advantage of the free water. Just include filters, so drip lines and stuff don't clog uop.
If you do above ground, you can also try aircrete, which is an amazing insulator and temperature stabilizing medium that's resistant to pests, molds, etc. Also hempcrete. Aircrete is lighter and cheaper, though.
Wish you the best!
