They all sound like great solutions, but are mostly long term which helps very little especially dealing with the invasion of biters your poor cows are dealing with now. Production more than likely also suffers in the mean time until the longer term solutions start to work to varying degrees. I'm not criticizing any of the solutions, I think they are great, and the right thing to do, I just know you can't sit and wait while your herd as a whole (even the ones not getting bit probably are annoyed or picking up on the unease/restlessness of the bitten ones, stress causes sickness, keeping sick animals with healthy ones is a good way for things to spread).
I know that you mentioned 1) specific oils being suggested 2) short term effectiveness 3) Doesn't last very long / wasn't very effective.
I'd love to hear more about what you've tried, specifically with safe volatile oil plant extracts and how you tried.
I don't have much experience personally with this as an issue, but I know Geoff Lawton has had success suspending a towel doused in strong smelling oils with ropes over his cattle laneway, and when the cows passed through, it coats them with a fresh application along the top of the head and back. I would imagine its not pure essential oils, but also added to another cheaper oil to lengthen the effectiveness, cheapen the per application cost, etc. So theres lots of ways to try and I'm sure with some research and discussion can find specific smells, oils, and additives that are safe and will help get you to the point where the long term solutions can be of use. Its always tough to know what the solution is, but not how to get there.
Hope this helps, and thanks for putting this out there for discussion
Edit: Forgot to add that for the irritated teats, I know that farmers have in the past and some still continue to this day, in fashioning a makeshift bra to cover the damaged/raw teat from exposure to insects. Sounds like this is a different area, but might be worth exploring if even to give her a few days to heal up without the fly exposure. Food for thought