Crossed posts, but I already typed this all out, so I'm going to push enter anyway
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There are some words of caution about the use of geranium oil, I've found with a brief search. Geraniums are toxic to dogs if ingested, but it appears that they can also suffer effects (vomiting, lethargy, rash) from just rolling in them. Not all dogs or people, but enough that it's reported.
Look up "essential oils safe for dogs" and "essential oils toxic to dogs" and you'll find some oils appear on both lists, such as lavender. The reason is because there's little control around these products, and little research. It may be that something is safe on a collar, but if they lick it off, it can make them ill. The dosage may be a factor: how much they can tolerate in one go, and whether there's a build-up over time. But there's no regulation, so no guidelines. No convenient pipette or schedule based on the weight of the dog. In the same way as eating grapes can have severe consequences for some dogs but appear to have no effect on others, it can be a lottery, so just because dogs A, B, C and D are fine, it doesn't mean that dog X will be.
Again, I'm certainly not pushing you towards conventional solutions, just trying to make the point that caution should be used when using other means. I feel for you because it's horrible being in a heavy tick area and not have a solution. And with Hattie's coat, I don't imagine it's a simple job even to say that you're going to give her a good check each day!
Have you discussed with your vet, to see if she has any suggestions?