There seems to be something organic for just about everything and I have heard of a couple things in the past that were supposed to work and were organic, but I couldn't remember what they were. After a little looking around I found that Diatomaceous Earth was supposed to work. Just make sure to ALWAYS use "food grade" as non food grade such as pool grade is just bad news for any animal that comes across it and is extra bad to breath in. I looked on youtube and found this video on a specific brand of DE that is used as an insecticide. https://www.youtube.com/watch?v=i2_G7jTgPKM
I suspected their product was just branded food grade Diatomaceous Earth so I emailed them and told them I wanted it to be pet safe. They told me their product is technically "food grade" but they cannot include that on the label once they call it an insecticide. They also said the proper term is "natural grade". Meaning the DE hasn't been treated. They said I can rest assured their line of products is natural grade and does not include any additives or synthetics.
Since I already have a 50 lb bag of food grade Diatomaceous Earth I think I may try that for the ants, but first I may try an insecticidal soap made with 2 teaspoons of Dawn Ultra to 32 ounces of water to kill any soft bodied insects like the aphids and see if the ants just go away on their own. Leaving the insecticidal soap on the leaves can damage the leaves (I think from drying them out) so they suggest test spraying the leaves first, but one guy said it only takes about 10 seconds to kill soft bodied bugs like aphids so he just leaves it on a few minutes and then hoses them off. Since these trees are in my yard I will just do the same instead of test spraying.
I thought about trying cold pressed neem oil but you should test spray that too (possibly because of the soap you need to put in it so it will mix with the water) and since I already have Dawn Ultra I will try the insecticidal soap instead. If I was doing an orchard in the woods I might try the neem oil but would probably try the Diatomaceous Earth instead.
I also read somewhere you can just sprinkle Diatomaceous Earth around the truck for ants, but I think if you mixed it with sugar it might encourage them to eat it which may increase it's effectiveness. I'm not sure.
I found the comment about the ants farming aphids by Brian to be both surprising and interesting. I never would have thought of ants protecting aphids to get the sweet stuff the aphids produce. You learn something new every day!