Its a myth that all low or at least most low SHBG guys are obese and diabetic. For a lot of us its genetic. My fasting glucose is in the high 70s to low 80s, I am not obese and supplementing with large doses of T3 and T4 (or in combination) still leaves me with a SHBG that ranges between 7 to 13.
I would try everything to see what may work best for you, but I would not hang my hat on loosing 10 pounds and taking some T3/T4 and have that get you to a normal SHBG level. I am not saying that to be a downer, either.