In my experience, carrots need deeply tilled, friable soil. It’s almost impossible to get it like that in my hard clay Texas soils.
My soil is very good, basically manufactured it myself. I’ve had great success with carrots in the past, even with saved seed from my own plants. I wanted a shorter season carrot however because I’m at 7,600 ft in N. Colorado and the season is cruelly short.
You will obviously be looking for much different varieties since you need heat tolerant plants and can grow the longest maturing plants available. Pinetree seems to offer something for every region though.
I haven’t had any luck growing them either...but our ground is perfect for making adobe bricks...
We grow carrots in containers. Had a great crop last year in a 40 gallon tote filled with plant mix.
Use a saw to slice a 2” cut into the bottom/side edge - 10 or so will allow the container to drain well.
We have our containers on a drip system but a single container is easy to water...and with the drainage slits it’s hard to over water.