Heat and drought how does a Mittleider garden fare compared to other gardening methods
Seeing that you will only have 2 or so beds I'd recommend the following:
Find out from your council if you are allowed to water your small veggie patch by hand (a bucket or watering can) during the days you are not to irrigate (sometimes restrictions are for automated systems that wet lawns and flower beds). If you are allowed, then watering two beds by hand is not too much to ask. (try not to wet the leaves of your crops).
If not, I'd consider attaching a water tank to the down-pipes of your roof gutters to make use of any little rain that may fall. You are free to use that water for drinking or irrigation. And maybe on your irrigation days you can fill up your tanks or containers. As a last resort I will consider using grey water.
Make sure you get enough sun. Having a sunny strip at a certain time of year does not mean that you will have it later, seeing that the sun moves N and S through the seasons. If shade may be a problem, consider planting more leafy vegetables that can ustilize the available light better.
If any trees are too close to the beds you might find their roots
competing sooner or later (besides the problem of shade they throw); you should be able to see their roots if they are present at the time you dig over your patch.
Keep to the recommendations of shaping the slightly raised beds. Once the veggies take off and fill their space they provide their own shade, just keep watering to make sure the soils stay moist. Veggies grow fast, don't have as deep roots as more woody crops and benefit by shorter irrigation cycles more frequently; there is no reason to irrigate deeper than the root zone as soil is not a reservoir for water. Too much water will only leach your minerals past the root zone.
Surprisingly, we have one more thing in common Diane - my landlord will not allow me to have a veggie patch anywhere. I found a wonderful alternative that, so far, works very well!
Where my wife works they had plenty of polystyrene containers/boxes!
Putting two and two together I realised that polystyrene (in our hot
climate) is a perfect insulation material. I find that they work much better out in the sun than plastic or even clay pots. They don't get cooked by the sun due to being white and thus provide good insulation so that the root zone doesn't over-heat or dry out too quickly.
I drilled drainage holes and now grow my veggies in them! The boxes are the perfect size and deep enough (8'' plus). I also have some in and clay pots and the polystyrene outperforms them both. Now it is not ideal growing in containers; having your roots have access to natural soil such as in Mittleider grow-boxes is better; but I simply have no other choice. I can also move my containers around to wherever the sun gets to them more.
I keep my containers raised off the ground in order to make sure
they drain well and to avoid diseases (Same as what you would do for
seedling trays or seedling flats). Simply lay them on some wooden stakes or something similar.
The only other crop I grew amongst some open patches in the garden beds (where they get enough sun) is climbing (indeterminate) tomatoes. They yield profusely and a few plants will see to our need throughout our summer this year. I grow them as single stems up a stake and keep any leaves clear off the ground. Cucumbers, climbing beans or other climbing plants can also be considered.
The FFEF website has ample instructions on how to feed plants in pots. For those people in flats or small court yards, I recommend trying out growing in containers. Herbs are of course an easy and rewarding thing to grow in pots. A little goes a long way and you can dry them (in your Excalibur Diane) and cook delicious meals.
Consider also that if you have a friendly neighbor (who might have a better patch of ground); you may want to introduce them to the Mittleider Method and share the fun of growing and sharing a garden together and sharing in the costs.
All the best with your pursuits,