Wow! Sounds like you have done your homework. I think you are right on all counts. I should have thought about thrips.
So yes, a dry mulch is better than green. If you are spraying with oil, be sure you get not only the undersides of the leaves, but the nodes where the petiole (leaf stalk) attaches to the stem.
Yes, in the long run what you really need is a garden in balance with beneficial insects and the plants that help attract them and maintain habitat for them in all their phases. All the carrot family plants are good for that, that includes the dill, anise, chervil, and fennel plants you mentioned and also angelica, caraway, coriander, parsley, carrots and Queen Anne's lace and others -- WHEN THEY FLOWER. These are useful for small beneficial insects, because they have flowers that have nectar in tiny florets. If you have one or two varieties from carrot family, you don't need to have them all. But you need to have a variety including other families. Mint family plants are good, including the catnip, but also regular mints (e.g. spearmint), pennyroyal, lemon balm, other culinary herbs like basil, oregano, sage, thyme. Some of the most frequently mentioned plants for beneficial insects are yarrow, tansy, alyssum, marigold, lavender, and milkweed/ butterfly weed.
So what you are looking for is a good variety of flowers for beneficial insects, representing several different families and blooming over different parts of the season and allowing the herbs to flower. Borage (aka bees bread ) is good for honeybees and other pollinators. I haven't seen it on the list of plants for predatory insects, but you certainly need pollinators also. If you have a variety of these flowers, you will have many benefits. Your garden will be beautiful!
It will draw in and nurture many beneficials, not only the ones that will help control your thrips; but also parasitic mini-wasps that will help control things like tomato hornworm, cabbage worms, and other such larval pests; tachnid flies that help control not only the caterpillar type pests, but stinkbugs, squash bugs, and beetles; hoverflies that help control aphids, mealybugs, and others. And you will be supporting monarch butterflies, swallowtail butterflies and a number of other butterflies. AND you will have lots of herbs for yourself - culinary herbs, herbal teas, medicinals.
But this is a longer term project. Now is not even the right time to be planting seeds, here in the heat of summer. Some of these could be planted later in the summer, maybe a month from now, for the fall. Some will need to wait for spring. In the meantime, to get a little start on this project, you could check out a good local nursery (NOT big box store) and buy yourself a few transplants of things like mint, marigold, lavender, culinary herbs.
Along with the flowers, your habitat needs to include water. Bird baths are good, especially with a few rocks in them to hold little splashes of water. A shallow flat water container at ground level is also helpful. Birds are also your friends in this project and having some bird feeders will help keep birds in your garden. And of course, don't spray any poisons! No point in trying to attract beneficial insects if you are just going to poison them. Poisons generally are much more effective against the beneficials/ predators which are much fewer in numbers than their prey and have slower generations.
In the meantime, the Neem oil is helpful for controlling a number of leaf-eaters and small soft bodied insects like your thrips. The diatomaceous earth (DE) is less likely to be harmful to the thrips, but is effective against a variety of crawlers including slugs and snails, ants, beetles, caterpillars. I use it against the slugs, except that it needs to be reapplied after rain and we have had nothing but rain this summer, so I gave up. But the DE can also be harmful to those beneficials, so put it on the soil around your plants, put it in those leaf nodes, but try to avoid getting it on your flowers. Any insect control measure is best used as spot treatment for where you see the problems, not broadcast around your garden.
Congratulations, on getting started on a whole new way of gardening - gardening with Nature, not against her. Once you get a garden in balance (which can take a couple or a few seasons, depending on how the garden has been treated ), it is much easier. You can relax and let your garden take care of itself!
