Learned a little more about why I scorched the leaves of my cherry tomato. Higher concentrations of soap (or in my case, probably detergents) not only kills soft-bodied insects by breaking down their waxy water-resistent layers, but also does the same to plants. This allows the soap to enter leaf pores and do cellular damage. This can be exacerbated by higher temperatures, full sun acting as magnifying glasses on droplets, and even minerals in the water. Apparently phytotoxicity – the degree to which a substance adversely affects plant growth – is a major concern of using soaps on plants, with some plants being extremely sensitive to soaps.
The upshot of this is that I should have tested a mixture first before spraying indiscriminately like a complete insecticidal fool.
A lot of good information can be found here, especially the reminders to observe the effects of a mixture on a small set of plant leaves and record the results.