Eek - have you tried Neem oil? I had Melon Aphids on my Strawberries and spent months trying to get rid of them. Honestly I never found a solid “organic” solution - but also never tried biologicals.
Well, I learned something:
“Aphids can reproduce both sexually (male and female, the birds and bees — you know the drill) as well asexually when the females clone themselves. This proliferation is even more amazing than you might think; not only are female aphids able to reproduce a new female aphid every twenty minutes, but the “baby” aphids often already have clones inside them. Three generations of aphids inside one aphid body is not just incredible but, for growers, incredibly annoying. Aphids spread through crops quickly.”