Considering your low T3, your FT4 is still a bit low, not horribly, but a bit.
You might try one of two things: a conservative dose of T4 meds (Synthroid, Levoxyl, generic levothyroxine). or a small dose of a T3 med (Cytomel). I think you want to get your HR up and your energy level up, and a T3 med is probably what's going to do it for you.
My T4 was 1.2 so it was in range.
In my opinion...not a doctor, just a fellow patient...NO, he is not right. Your TSH is clearly hypothyroid (currently accepted range is 0.3-3.0 - your doctor and lab are using archaic range). FT3 is below range and therefore also hypo You didn't give FT4, just range.
Your low HR is also a symptom of hypo. 50 or less for a resting HR indicates bradycardia...it's too low.
You need to have your doctor start treating you based on FT3, FT4 and TSH, in that order. You can try to educate him, but you might also have to be prepared to find a doctor more knowledgable in thyroid.
Six to 12 months is way too long to wait. You need treatment now..
I think you left out the free T4 result; however, even the free T3 and your symptoms and the high TSH results are enough to diagnose hypothyroidism. I have no idea how your doctor can say you do not. If he places a lot of emphasis on TSH, is he not aware that the even the old range for TSH was .5-5.0 and the AACE has recommended 6 years ago that the range should be reduced to .3-3.0? I think you are going to have an uphill battle on your hands to get this doctor straightened out enough to put you on thyroid medication. I suggest that you don't wait around, but start looking for a good thyroid doctor.