A naturopathic/holistic doctor would be more likely to be willing to treat you by symptoms rather than by TSH levels, since TSH is pituitary hormone, not a thyroid hormone...
Just as important as TSH and Free T4 is the Free T3 thyroid hormone. Free T3 is the active hormone, used by individual cells, whereas Free T4 is considered a "pro-hormone" and must be converted to the active Free T3. You may have a conversion issue, or an absorption issue.
Have you had ferritin, vitamin D and/or vitamin B-12 tested? Vitamin B-12 deficiency can cause debilitating fatigue/tiredness and one can actually be deficient, even if labs say your level is within the normal range, since the ranges are so broad. The same is true of vitamin D and ferritin... Ferritin is the iron storage hormone and without adequate stores of iron, we can't convert Free T4 to Free T3, plus iron is necessary for adequate energy.
If you have results for those vitamins/minerals, please post them, so we can be sure that your levels are adequate - not just "in range".
I should add there are doctors who will treat patients with TSH in range. Gimel (another medhelp member) has a list of doctors who may be able to help you.
I could not get any GP to prescribe thyroxine until my TSH rose to 6. Labs in Queensland, Australia dropped the TSH to 4 mU/L a few years back but it's still too high. Studies have shown most healthy people (without thyroid symptoms) have a TSH under 2.5 mU/L.