There is an OMRI-approved biological pesticide called Mycotrol that uses a fungus, Beauveria bassiana, to kill root aphids in container crops. Johnny's, Peaceful Valley, and a few other sell it, but it's expensive.

I often see root aphids clustered on dandelion roots when I pull them out. With those peppers, I'd drench the roots with soap solution and then mound up soil and mulch to change the microclimate.

The root aphids I had were farmed by ants and controlling the ants stopped the spread of the aphids. I also tried a soil drench of a neem solution that seemed to help with the aphids directly. Aphids on roots are indeed an unpleasant surprise. Good luck!

Thanks! I think I'll go with a multipronged approach and try a soap or neem drench, mounding dirt, and ant control.

Wait. Don't start with the kiling agents. If the aphids prefer the dandilion roots, DON'T pull the dandilions, and espcially don't try to treat them with some kind of toxic herbicide or aphid killer. If the aphids are on the roots of the dandilions, that does NOT mean they are on the roots of your other plants. It is possible that keeping the dandelions, the roots of which would be the aphids favorite food, is helping to keep the aphids from looking for plants that they don't like as much. If there are aphids on your other plants, the best thing you can do it let the dandelions thrive, so the aphids don't have to move to less-preferred food sources. Watch this video - and pay attention specifically right after 4:00 minutes - and keep watching. He will talk about DANDELIONS!! Listen to the experience. https://vimeo.com/98940910

of course your crisis was 2 years ago, but maybe you will be able to apply this knowledge going forward.