Since you haven't gotten any suggestions here, you might try asking in the California forum which seems fairly active since there will be more experience with your particular growing conditions. There are also forums (fora?) for AZ, the southwest, and TX that may have ideas for you, especially if you do a search for "vine" in the box at the top and then click on the "vine in Arizona" option when it pops up to restrict it to just the one forum.

I do wonder about the restriction to containers since the containers will kill whatever groundcover is under them. If you do go for this option, use the absolute largest containers you can find to reduce temperature fluctuations, and choose a light color to reflect rather than absorb heat. Water management will be a challenge. I sometimes use large saucers under containers that I can fill with water that the container's soil can wick up as needed.

Thank you! I will check in the California forum.

There is gravel up the wall, so there isn't any groundcover to kill. I like the idea of wicking, and am considering a drip system or making "wells" with a plastic bottle to help with watering.