dish soap always works for me, maybe your solution needs to be a little stronger. I put 1-2 tbl spoons in a 1 gallon sprayer and don't spray in the hot sun. I use the cheap dish soap from the $ store. That should suffocate them.

Lacewings should help. The catch is that the most cost-effective form is eggs, and they take a couple weeks to grow up into delightfully murderous little buglets.

It is too cold for lacewings. Have to wait until it is getting over 90F.

I buy the liquid detergent pesticide in the garden enters. Made and formulated specifically for plants and usually runs under $7 a squirt bottle. Dawn works well for homemade, but I do not like the imprecise nature of homemade remedies as it can harm your plants.

I have already noticed lacewings in my yard, but I am still going to spray the pomegranate where the ants are farming the aphids. I will look for the detergent pesticide when I stop by the store today. Thanks!

It is too cold for lacewings. Have to wait until it is getting over 90F.

I've seen them already in Phoenix. They showed up right after the first few aphids on the tomatoes.