Intolerably hot summers but perfect winters here.

Stats: Mediterranean climate (South Australia). Heavy clay soil. Cool rainy winters. Extremely hot dry summers without rain or humidity.

Winter: My yard's amazing at this time when it's blanketed in thousands of spinach, parsley, dill, lettuce and other plants through self-seeding. Steady rain sprouts seeds and grows plants which easily push roots through soft wet clay. I don't have to do anything, food just grows for me.
Spring: All the plants go to seed immediately, becoming pretty useless for eating.
Summer: Just about anything planted in my yard- new or old- dies from unbearably hot sun and lack of water. I sweat immediately just from standing there. It takes forever to water the yard with a hose, and it doesn't even penetrate the surface anyway. The chop-n'-drop plants don't decompose without water, I can't give access to a truck to offload free mulch, and digging anything into the soil seems to just disappear as clay 'eats it' and it becomes invisible. I really hate summers here, and so does my clay soil which turns into a lifeless brick.
Autumn: A moment of rain brings new seeds to life and the cycle repeats.

Plan for next spring: (1) Invest in an irrigation hose with sprinklers with an electronic timer to water the entire surface of soil twice a day. This is the hardest for me because I have no practical skills so will probably do it wrong. (2) collect any organic matter possible to try mulch the soil. (3) Chop-n'-drop all winter plants early spring and immediately replace with seedlings to establish roots before summer.

I feel you except my dry clay soil happens in winter and it's cold cold cold so I can't grow anything in it anyway. Nothing decomposes.

You might consider a dense planting of moringa, to create a fast growing canopy to cool the earth. You could chop it back at the beginning of the rainy season, and by summer it would grow back to protect your understory plants. You could use all the cuttings to cover the soil. You could get thousands of seeds fairly cheap on the internet. And if it was me I would cover everything right up to the house, it will help cool your place and keep water from evaporating so fast.

Your Moringa suggestion is interesting! I didn't bother planting moringa in the past because it probably wouldn't survive the cold (frost-free) winter here. But if it's intended to be cut down every winter then that could be ideal.

Would the Moringa roots compete for nutrients with the other plants?

Parts of my clay soil seem to be turning into loam already by cutting down densely-planted spinach and other plants but leaving the roots in. Over the yeras I'm pretty sure it'll all turn into loam.

Moringa will survive the cold.  If it doesn't frost, it won't die back.  If it does frost, established Moringa will die back to the ground and grow back when it gets warm again.  You will need to protect the young trees during their first few winters so they can become robust enough for the roots to survive winter on their own.  My plan for this hot summer climate is to grow Moringa throughout my gardens for shade during the hot season.

http://www.thesurvivalgardener.com/growing-moringa-q-yields-maturity-fros/

https://www.youtube.com/watch?v=Ab2NWyGvuwA

No it won't compete for nutrients, it's actually a dynamic accumulator of nutrients. So every time you chop it back it will shed roots below and give mulch for up top, as well as one of the most nutrients dense foods on the planet. As well it sores water in it's  trunk and is extremely drought  tolerant. It has a sparse canopy that allows filtered light. This guy in Arizona which has similar baked clay soil and heat, as well as occasional frost, has used them for the basis of his food forest with excellent results. I'm using it similarly here in Florida. Though mine is still in it's infancy.
https://youtu.be/PF3xrtMppQw

Also it can handle light and brief frost. It takes a good hard freeze to kill the trunk once established. Even the leaves have been known to survive the briefest frost.

Moringa gives very partial shade. If you want a dense shade fast, plant chaya. I use both in my property, but chaya grows faster and is easier to multiply: just stick a stick in the ground.