Some of those will just be fried in the full summer sun, as they would be here in Central Texas. In a container that's in sun, the soil doesn't have the heat sink of the Earth to help moderate the temperature. And when I began building self-watering planters, I realized just how much water a plant can demand, which was a lot more than I had previously been offering them by hand watering.
It may be impossible to not have a drastic wet/dry cycle without frequent hand watering in summer sun. Once roots dry out, it's a real bad deal for the plant. Remember that you changed their environment when you brought them home, so they're under some stress in the best case. Considering your description of the location, I suspect heating and drying is the problem. You may need to give them some shade in summer, at least until they are bigger. Sun shades can be had in squares and triangles, with grommets. Or just as shade cloth, which is usually less drastic shade, because the others are meant to shade people, and shade cloth has to pass sufficient sun for the plants' needs.
They make some things now that are a variation on a Forsyth pot. It's a clay sort of nipple that screws on the end of a bottle. You stick that down in the soil, and the soil takes what it needs through the porous clay. I haven't used them, but I do use Forsyth pots for rooting, and it's surprising how quickly the can empty the clay reservoir. Look for "watering stakes" on Amazon. There are also mini drip devices and slow watering bulbs for containers. I like the clay things, because it delivering water to the soil's demand.
And a substantial proportion of vermiculite mixed with the soil can retain water and release it as needed.
And they might indeed need to be repotted. Store plants are often root bound in the nursery container. If you think about how the plant only has so much root exposed to so much soil, a plant whose foliage has grown to match it's root volume may have relatively little soil to draw water from. I consider this very important. Here are some calculations:
A 4"x4"x4" container of the seedling size is 1 litre, 48 cubic inches.
A 6" pot is 3 litres.
An 8" pot is 6 litres. 383 Cubic inches.
If the plant was already in an 8" pot, going to a 12" pot takes the volume up to 21 litres!
Which would you like to live in, if you had to depend on only the soil in the pot for water and nutrients?
I assume for most things, that the nursery used the smallest workable pot to keep shipping and display expense down and that almost everything needs more root space and likely has exhausted the small volume of soil provided. And if you note that the volume grows far faster in proportion as the surface increases, and the difference is greater, the greater the size of pot, there's better heat management.
And a deep mulch can conserve moisture. Many mulches should not be in direct contact with the plant, but even nice round stones, available from a landscape supply, will help, and white ones will reflect at least some sun.
I suspect you're not far from success but have just tipped them over the line of what they can tolerate, with maybe a combination of heat, bound roots and drying, and even some small changes may make a great difference.
