Wow … only 150 mcg a day? I am surprised you can function. I had RAI 30 years ago and have been on 90 mg daily since … I switched from synthetic to dessicated thyroid- Abbott’s NP thyroid about 15 years ago. I have no other heath issues and have never had weight issues either.
It is difficult to fathom how your TSH/T3/T4 levels are right on that minimal of a dose. I am 61 and other than a low Vit D one time, all my extensive blood tests are excellent.
Something does not sound right. Have you always used the same phlebotomist? You said you still had a bit of thyroid gland? I would switch doctors. Do you see an endocrinologist? If nothing else switch to a natural thyroid medication.

I am just seeing this years later. I was going to say take iodine? just iodine.

maybe you need pig thyroid. your medicine has only 1 of the 4 hormones your thyroid used to make. that is T4 which requires your liver to convert to T3. If your liver can’t do it then you need to take T3.
Find a compounding pharmacy in your area and call them and ask what drs are in your area that prescribe natural thyroid. that is what I did. Got my life back. I have the same low thyroid symptoms you have but on a much more manageable level. Natural thyroid gave me my life back. Damned endocrinologists refuse to prescribe it and God only knows why. they want us to be miserable?