I think you will find that your soil is alkaline. Not many things like alkaline soil. When pH is high micronutrients become less available and nitrogen volatizes off quickly.
Your water is probably also alkaline.
This is the Arizona vegetable guide from the Arizona master gardeners with the types of plants you can grow and the planting dates for them.
https://ag.arizona.edu/pubs/garden/mg/v ... guide.html
If you are only adding Kellog's you need fertilizer too. It would account for the small plants if nutrients especially nitrogen is limited. The best way to know what and how much to add would be to do a soil test. Instead of Kellogg's I would probably use peat moss instead. Peat moss that has been limed has a pH of about 6.0. Kellogg's and other aerobic composts will be alkaline and that won't help your already alkaline soil. Sulfur would be futile but using an acidic fertilizer won't hurt.
Manures can be problematic since while they are good organically they contain a lot of salt.
If you contact your local master gardener and ask about where you can get a soil test. Ask about the cost. I looked online and apparently Arizona soil tests cost more than other places. A basic soil test costs me $12 in Hawaii with recommendations.
https://extension.arizona.edu/sites/ext ... 20CALS.pdf
I think your garden will benefit from shade cloth 47% shadecloth at least 8 ft high.
Trickle irrigation is best but it is usually slow so your watering time should be extended. Compensating drip emittters deliver a set rate but are usually left on anywhere from 2-10 hours. It all depends on the type of soil you have. If it is sandy, it needs to be on longer. I would check the depth that is wet at intervals and water until the soil is damp 4-6 inches deep. Mulching will conserve water.
I think your plants need fertilizer adjustment. I don't have your kind of soil conditions. However, I have told people who live in areas that are built over coral not to fight the soil. Plant acid loving plants in containers with potting mixes. You can manage pH in a pot but you cannot make alkaline soil acidic.
If you have decent sized greens but fruit and roots are small, that usually means there is too much relative nitrogen. A couple of weeks before planting add 1/2- 1lb of 10-20-20 plus micros over 100 square feet. For your bed size of 32 sq ft 8x4 you probably only need a handful. 1/4-1/3 cup. I would only use miracle grow for the first month while the plants are small and actively growing, then stop. Root crops benefit from bonemeal about 3 weeks after they germinate and before they bulb up.
The bed is too small for all the plants you have in it and that may be part of the problem. If you use square foot garden planting plan.
This is close to what I would plan for that small a space. The program does not allow me to adjust position so I have to make do with what is does allow
https://www.gardeners.com/on/demandware. ... C=XNET9436
Two tomatoes - they are better if they get 4 squares instead of 1. 1 square requires a trellis and a lot of pruning which would not be good to cut leaf cover in the arizona sun. I cage my tomatoes. Less work.
Between tomatoes while they are still small and the weather is cool enough under 85 degrees you can grow butterhead, red and looseleaf lettuce. Once the tomatoes size up there won't be much room.
Beets, radish and turnips do not take up a lot of space and can be intermplanted. they need about 4 inch spacing. I plant 21 day radishes around the young squash, tomato, eggplant and peppers since they don't need the space until they are bigger and by then the radishes will be harvested.
zucchini and summer squash bushes take up a 30 inch circle so only 2 plants in a 4 foot width and part of the plants will be outside the garden
Cucumber can be trained up a stacked tomato trellis. I have planted 4 on one trellis. It is the only way to keep them inside a square.
Hot peppers can take the heat and will fit inside a square, but they are tall so plant shorter plants around them.
vining crops are planted on the end and the vines will sprawl outside the garden. You can pile vines on top of each other.
Herbs can be dropped in where ever there is room. I would wait until the other plants have sized up to put them in since they also do well in pots for a while and to make sure there is room for the other plants to spread. I plant them in pots and just place the pots in the garden It makes watering easier and the pot placement can be adjusted based on the space the other plants take up. basil can get tall so you may have to figure out the best spot for it.
This program did not allow for flowers but you can also grow borage, sunflowers, marigolds, alyssum, baby's breath, zinnias and other cutting flowers between the plants. They will attract beneficial insects.
Lettuce is a cool season crop and it will bolt in the heat so it has a short growing season It does not like weather than exceeds 85 degrees.
Happy gardening in Hawaii. Gardens are where people grow.