I can tell you how my own thyroid hormone doc explains rT3. It can be high for more than one reason. They claim that treating thyroid with Synthroid (T4 only) often makes it worse, which they called "reverse T3 syndrome." (Side note, Dr Kruse would call it leptin resistance, which is another way of looking at the same numbers).
Not everyone wants to agree that reverse T3 syndrome is real, but that's just a debate for theory, we want to get better and want to know what to do, who cares who is right!
Other main causes are toxins and the big one-starvation or yoyo dieting. A good endo should understand this about yoyo dieting or get out of the way. That is real. This is why I hit the ceiling when I saw so many Paleo folks telling people on weight loss stalls to do IF. That's the worst idea since food reward if you have high rT3.
You don't just lower rT3 directly. rT3 is part of your biology to protect from a famine situation by slowing metabolism, and it just sticks. You fix the problems and allow T3 to take over instead. How to do that?
You need a real dr, and may have to bite the bullet on insurance. I'm paying most of mine out of pocket and it's expensive, but I like having 120 lb gone so I'm sticking with it. I do plenty of supplements too, but they are based on blood test results and I see the changes, so I don't feel duped into buying a lot of "medical food."
A dr that will dismiss your concerns about rT3, refuse to consider using natural T3 instead of a T3/T4 combo from big pharma, or not test adrenals (cortisol, testosterone/progesterone) and know what to do with them is not going to ever get you very far.
Low carb will help, but it will be miserable and you end up thin and still sick.
You can find plenty on rT3 in leptin books, and a little in thyroid books, but thyroid folks typically don't get it. One thing they have in common is they are into low carb, more protein than most LCHF folks do (at least while you are getting better).
What worked for me is this-
-Switched off T4 (Synthroid) and replaced it with T3 from a dispensary.
-For adrenals- DHEA, testosterone, and for a while cortisol (because everything shut down).
-Low carb, lean protein in the beginning.
-For insulin resistance, and to boost immunity, two different extracts of maitake mushroom, Vit D, and omega 3 fish oil.
There is more info on my blog on the my diet and plan page. Standard disclaimers apply of course.
The problem of finding a good dr can be maddening, but it may be the only way out. Mine is in Ca, and I live I Memphis. I'm not switching to anyone local.
Good luck and feel free to ask more. I hate to read about others going through this too.