I would recommend embracing the clay, especially if it gets super hot and arid there. I would be more concerned about the pH. Nevertheless, organic matter is important, but changing your clay into something else is a lot of work and expense (and can take years, which you might not have if you're moving).
Here's what I recommend:
- Mix peat moss into your soil before you plant. It has a pH of about 4.0 (acidic) and it's bulky with organic matter. There's also some kind of acidic bark you can get that some people like. I'd recommend either of those over adding sulfur to acidify. The organic matter won't last forever, but it works for at least a year.
- Add some composted manure or such. You may or may not need to add potassium with it, depending.
- Add some sand, if you have some handy. Some people don't like sand in clay, but I personally do. The type of clay probably matters (not all clays seem to be the same). So, test it out before you add too much sand, and see what you think. Greensand and gypsum are supposed to help loosen the soil, I believe (but that may be expensive, and may or may not work as you expect).
- Grow some peppers in moving totes. Jalapenos and many other peppers seem to love it, if they have the right kind of soil. Large bell peppers might do better in the ground, though. Many people will tell you to use a certain kind of soil for containers. My advice is to use what works in your garden. Try what people suggest, and if that doesn't turn out well, try other stuff, too. Some of what people tend to suggest hasn't proven efficacious in my garden (but some stuff they advise against is great; I think what they suggest probably works for most people, though).
- Mulching might help (to help lock in moisture, attract worms, and block the sun from the roots more). Many mulches will raise soil pH, though (probably for the reason wood ash raises pH). Find one that is either neutral or that lowers it, making it more acidic, if you mulch. Some mulches (such as hay) may introduce weed seeds (same for some manures). Hay may add such as extra nitrogen and calcium, though.
- Don't grow apples (they're not the easiest things to grow for fruit in the desert, even if they're popular), especially if spider mites are in your area. You might try apricots, plums, peaches, almonds, figs, dates and stuff like that. If you want to grow apples, get a good variety for the desert, water it enough, mulch it, don't get spider mites, prevent worms, and don't let fallen fruit rot (especially if you have spider mites).
- Know when to garden. The hottest part of the year isn't necessarily the best, especially in the south and southwest. (It's a great time to garden in my area, though, even when the daily highs are constantly between 90° to 116°.)
- For perennials, choose those with low chilling requirements. I mean, if it needs a longer winter to fruit well in the summer, you might want something else. Similarly, get plants that like the day length you have. Southern areas usually have fewer daylight hours than northern areas, and that matters for some plants (like onions and Shark Fin Melon).
I also recommend finding plant varieties suited to both clay soil and your area. Nativeseeds.org may be a nice place to visit, especially for the southwest. They have a list of varieties suited for heat and drought. Here are some varieties you may enjoy:
- Dark Star zucchini (zucchini generally is good for growing in clay soil, but this is a particularly nice variety; I grew it this year and it did well; you might try squash generally, too; it can usually handle clay; watch out for squash bugs; maybe try Zucchino Rampicante and Cushaw White for something squash bugs don't like—but I haven't tried either, yet)
- California Wonder peppers (I hear they can handle clay better than most peppers; I would grow these in the ground rather than containers, though)
- Mulberry trees (you might like the weeping mulberries, since they're smaller; I hear mulberries grow well even in caliche)
- Cantaloupe and muskmelons generally can do decently (not sure about in the southwest, but they're usually more adapted to dry heat, cool nights, and clay than watermelon)
- Red-seeded Citron watermelon (this is an exception among watermelons and is well-adapted to the desert and at least clay loam soil; it doesn't taste like the watermelon you're used to, though; I recommend using it as a replacement for water chestnuts in stir fry, if that gives you an idea of its taste and texture)
- Amaranth loves clay and heat
- Thessaloniki tomato (heat-tolerant, decent-sized and productive, especially for the size)
- Camp Joy tomato (one of the most heat-tolerant tomatoes, I've read).
- Amana Orange tomato (I'm not sure if it likes arid heat, as it was a late tomato that I started too late, but it grows astonishingly fast and big in clay soil, in my experience—not just clay loam)
- Yellow/Red Pear tomato
- Aswad eggplant (If any eggplant will work in your area, Aswad is a likely contender. I grew it and it did well for an eggplant. I saved lots of seeds if you want some: just go to my website and contact me from there if you want some. I have lots of other seeds, too.)
- You might try such as Crimson Forest bunching onions. They seem to germinate and grow well in clay in my experience (I'm not sure how they handle strong sun and drought, since mine were shaded and well-watered).
- Cacti (there are lots of fruiting varieties; you can eat the pads of many cacti, too; look for productive kinds that taste good); cacti probably aren't the best choice for clay, but I'm not sure how much that matters in the southwest.
- You might try smaller or narrower, productive, peppers (e.g. Ring of Fire, Corbaci, Tabasco, and Aji Omnicolor); they may do better than most peppers for you.
- For cucumbers, you might try Beit Alpha or Armenian cucumbers (Armenian cucumbers are really muskmelons, and muskmelons may prove easier to grow in the desert, depending if cucumbers like your soil)
Another thing I recommend is saving your seeds to grow again, every year (unless you're growing hybrids and want the same hybrids next year). Saving seeds should help your plants to become more acclimatized to the growing conditions (air, soil, heat, sun, etc.), especially if you didn't get your seeds from someone who grew them in similar conditions. Saving seeds is especially important with stuff that didn't do well the first year. I've noticed that this seemed to help quite a bit with my Ledmon watermelons and Morelle De Balbis (which didn't do that well the first year, and did much better the next from saved seeds). You may even notice changes in taste between the years (I did), as well as heat-tolerance, number of seeds, days to maturity and such.
If your tomatoes are acidic, you might add extra potassium. This should help with fruit size, water uptake, and heat-tolerance, too. If they don't grow fast enough, they may need extra organic matter, nitrogen and water. You may or may not need extra phosphorus, too (it helps with lots of stuff, like flowers, fruit, growth, seeds, and plant maturity).
I've found that showering plants with a shower nozzel or sprinkler helps them grow faster and keeps pests (aphids and spider mites--and perhaps whiteflies--in particular) at bay (but I only suggest that for semi-arid to arid areas where your water isn't hard or corrosive to plants' leaves; showering plants might contribute to fungal disease in temperate and more humid areas, or during cool, wet periods).