I know you'd feel so much better with Free T3 at the top of the range, or at least in the top quarter of the range. Beware if a doctor wants to give you only T4 medication, as it might drive Reverse T3.
A way to sort through whether you have adrenal issues as well, when your schedule permits --
For 5 days, take temps 3, 6, and 9 hours after arising. If you arise at 6 a.m., then temp at 9 a.m., 12 noon, and 3 p.m. Average the temps each day. At the end of 5 days, you want to see no more than 0.1C variance of the 5 daily averages. For instance, each of the daily averages might be 36.8C or 36.9C, but not higher or lower. If the averages aren't tight together, you can add adrenal issues to your list, likely the result of long-time weak thyroid function.
You seem to have your issues well in hand, though, and I regret you face a problem made difficult by product restrictions.
Do you mind sharing where you are? I'm in Texas, by the way.