its admirable to be so against using any foreign agents on your plants randall but really a little soap is so innocuous as to not matter.
i have used a mild soap spray on my veg for thrips and the plants far from suffering will thank you for getting rid of the hitch hikers.
there are plenty of commercial sprays that are very kind to the plants and derived from plant extracts themselves and its also possible to make your own insecticide if you dont want to spend out.
its been a while since i had my own garden but i used to treat infestation with homemade sprays (as well as companion planting)
boiled up rhubarb leaves are an effective organic insecticide as well as a brew made from old cigarette ends ( the rhubarb spray is a much nicer thing to make tho

)
if you are getting to the stage where you have to remove leaves because they are so infested then you need to intervene with a spray for the sake of your plants (imho)