First things first, contrary to my username I'm not an MD. (sadly, my username used to be "World's Greatest Lover" but I wasn't that either....)
I take levothyroxine which is synthetic T4.
I would take care of your hypothyroidism first, then retest T and E. The thyroid is relatively simple as far as organs go and well understood. Results are easily measurable both clinically and from a patients QOL standpoint.
While the AACE doesn't necessarily support treatment unless TSH > 5 and there is evidence of a goiter or anti-thyroid peroxidase antibodies, they do feel that with treatment, TSH should be brought down below 3.0. I think with a list of symptoms that match subclinical hypothyroidism as well as an elevated TSH, a cooperative doctor could be persuaded to start levothyoxine treatment.
From my own personal experience, I walked in to my docs office with my labs showing TSH between 4.6 and 5.2 and he started me on 25 mcg immediately.
You can also check out the "stop the thyroid madness" website, however, I found it's tone to be a bit off-putting. I certainly wouldn't bring in articles off the site to my doctor. Instead, I'd use it to do further research.