Browse Hummert's website, and or your local Ag Extension website. There are many newer pesticides out there. Some are systemic and are NOT neonicotinoids. I don't have time to do it for you. But some of the new ones are biological derived products like the Abemectins and such, way beyond the Bacillus thuringensis derived products. So do some reading.
www.hummert.com
If you stick to soaps, key to effectiveness is the repeat spraying, and read what is recommended on the label for repeat interval. The higher the temperature the less time between repeat applications for effectiveness. I think once every two weeks is not frequent enough, especially in warm weather, but you need to do the research.