What has your clay soil been amended with to date?
Finding enough organic matter to amend the clay soils in San Diego can be problematic since you do not have a lot of deciduous trees around to contribute their leaves. A number of people in your area use wood chips which do add some nutrients, but the only way to know what nutrients your soil needs is by having a good, reliable soil test done, especially sine you need to know the balance between Calcium and Magnesium in your soil.

Kitchen scraps are free. Compost first in a pile or bin, or use a more direct 'sheet composting' method.

When I first moved here, the yard was an unkempt mess of weeds that were 2 feet high. Because the yard had been neglected for so many years, the weeds actually naturally composted down into the clay soil so the soil wasn't that bad. There were a lot of weed seeds, so we solarized it by covering it with plastic bags. I tried clear plastic and black plastic, and the black plastic worked. The clear plastic just had a green house effect, and did not work. The heat of the sun killed off the seeds and living weeds. This took 6 months. Then I dug up the soil, about 1 and a half feet deep, and added Kellogg's Amend. That was two years ago. I have only added mulch to the top of the soil, and the red cedar decorative bark. The plants are thriving, but I want to make sure the soil doesn't get too dense, since it's been a couple of years since I've amended it. I've been adding earthworms that I find under plant pots, and that seems to help.

I am hesitant to use kitchen scraps or anything else that would attact vermin or pests, because I live across the street from a school that has giant cockroaches. I also have rodents and opossums.

Organic matter must be added to any soil continuously and forever. It is organic matter that the Soil Food Web, including earthworms, live on in your soil and as they disgest that OM and convert the nutrients that it contains to the plants growing the OM "disappears", is consumed, used up, and must be replaced.
Any vegetative waste placed on your soil as a mulch will be converted by the Soil Food Web into the humus your soil needs and if composting is not an option for kitchen waste now that can be buried in your soil, not just placed on top, with good results.

Kim, agreed. By kitchen waste, I meant fruit & veggie peels & scraps, not leftover pork chops. The plants don't care if you buy mulch or make your own.