How well is your Addison's being controlled?
Adrenal insufficiency can cause your adrenals to force your thyroid to slow down. Your Free T3 really needs to be closer to 340 or 360.
IF your adrenals are suppressing your TSH to slow your thyroid down, the normal procedure is to get your adrenals back in shape first. Otherwise, the thyroid medication can backfire and make you ill.
You need to figure a way to find a happy medium here, so that you can get some support for your Free T3. Having your Free T3 that low is not healthy at all.
Sounds like you might need a better Endo to sort it all out.
What is the best way to support your Adrenal glands?
I take a full replacement dose of hydrocortisone which is 20 mg in the morning and 10 mg in the afternoon. I feel better knowing that someone else thinks something is off here. My endocrinologist talks to me like I don't know anything, but having addison's for so long I've had to do a lot of medical research on my own.