I'll ad my 2 cents to this old thread.
I never use essential oils as a treatment or medication. I only use it as a lure or attractant for my sugar blocks, protein patties or swarm traps. Never in syrup. So the fact any oils won't blend into liquid without separating is no matter for me.
If they won't take up syrup, there is something up. Ether they have natural feed sources that are better or they have a hive issue. Queenless, no brood, heavy mite or disease load, etc.
Sometimes about this time of year I have a few smaller colonies that are slow to grow and are reluctant to take up syrup. But you have to figure out what their issue is. Sometimes it is just that they don't have enough bees to generate enough heat to get the brood nest started. Sometimes it just a lack of enthusiasm. They eventually grab a gear when natural feed sources kick in. I've found no amount of lure or attractant additive will help that, although I do lightly sprinkle the top of the frames with light syrup on occasion to try to inspire them to take up supplemental feed.
I use Mann Lake's pro health on occasion, and if I wanted to stretch it, I would just add a pint of Pro health or Honey Bee healthy to the recipe shown in the op. I bet it would blend up nicely and stretch your dollar.
I'm careful with essential oils. Just touch a tiny drop to you lips and you'll know why. A little goes a long way.