I helped make kimchi once and it was really hard work, but it was great to eat it when it had fermented. Your garden is doing great. Maybe a compromise with chemicals would be to just use less than what other people use. I can imagine that the bugs love cabbages. I'm sure you could find a natural solution, but it would probably be a lot of work and might not do the best job.
Kimchi making is good fun once a year. I wouldn't want it to be my full time job.
The local farmers have been telling me that I'm either feeding the bugs or using chemicals. It was probably sprayed last year before I took over and if they spray, I'm going to get residue. I'll use as little as possible and wait until the plants are large enough to survive.