Scientific studies have shown that Free T3 correlated best
with hypo symptoms, while Free T4 and TSH did not correlate at all. If the doctor
still resists, then you should again insist and don't take no for an answer.
If that fails, then you might as well find a good thyroid doctor. A good thyroid doctor will treat a hypo patient clinically by testing and adjusting Free T3 and Free T4 as necessary to relieve symptoms, without being constrained by resultant TSH levels.