I am glad that you have been able to do some research that is helping to overcome your problem. I have had the same problem with Yogi for over 3 years, symptoms very similar, and the vet was unable to put her finger on the problem as well. The only thing she could think of was possibly dust mites, and it didn't fit the symptoms, and the action of the cat. We checked for fleas, and couldn't find any. With 5 cats all clean, and free of fleas that ruled that out as well.
My solution to the problem was very much by accident. Some of us were involved in a post back in August regarding coconut oil and its benefits. So I decided to try it on the 5 cats, and was surprised at the results. The cats' fur took on a good healthy appearance, and when being brushed you would get very little shedding hardly worth mentioning. It wasn't until about 2 weeks after I had started or maybe a little longer I realized Yogi wasn't showing signs of his symptoms like he was before, and if he did they weren't as severe, and they were short-lived. I had also picked up Yogi a new toy about the same time to replace his old one called Cat Charmer which he thinks the world of. This ended up causing more interactive playing between all the cats and myself which I think helps to take his mind off the problem.
You might think of using coconut oil, and see if this will help. I started with a very small amount maybe half the size of a pea about 3 to 5 drops in their food to start with, and very slowly increased the amount of drops over time so in about a month to 6 weeks they were up to a 1/2 mL twice a day on their food. The coconut oil I use is one that was recommended in a post on this web site. It is called Nutiva. We use it ourselves. When I started to use it, I warmed it in a little jar in some warm tap water, and then dripped it onto their food.
I ran into a lady in our local vet's office a few days ago, who uses it all the time with her cats and she just puts it in a bowl on the floor and the cats help themselves.
In regards to the Tea Tree Oil, I would stay away from it because it's an Essential Oil, and can have adverse reactions on some cats. It is a Microtoxin to cats which has been known to cause irreversible damage.
I will include a web site to have a look at as well as the post from August regards the coconut oil.
As far as "fish oil" is concerned. I use Salmon Oil by SISU, and the reason for this is because most fish oils have Anchovy in them, and this again is not good for cats over long term. To my knowledge, SISU's product does not have Anchovy in it, just Salmon Oil. It is a softgel, so I usually just prick it with a straight pin and put 4 or 5 drops on the food twice a day - when I use it. It is not something that I give all the time. And I didn't find that it helped with the "rolling skin" syndrome either. And it didn't have as good an effect on the fur and dandruff like the coconut oil does.
Going over Yogi's history the last 2 years, I am wondering if stress has been some kind of an issue aiding in his FHS. It appears as though he perhaps has been under some stresses that I was unaware of, with a multi cat household, and moves. He has also had some issues with power tools being used from time to time. He doesn't like them. It has taken him 2 1/2 years to get over a Router.
By the way, I was talking to our vet on Tuesday about this problem, and in all the time she has been a vet - over 15 years - she has only seen it once. Luckily there was another vet working at the clinic at the time, and they recognized it, because she didn't. The problem being, by the time the animal has arrived at the vet's office, the issue has settled down and doesn't appear. It's like us going to the dentist office for a toothache, but by the time you get there, the ache is gone. Ideally, it would be good if the vet could make a house call almost immediately.
Something else to consider is food quality. It can also play a role in the problem.
Please let us know how things progress.