You really can't know if the flip to hypo is just a normal result of postpartum thyroiditis, or if it is due to the Thyrosoothe, which from what I read works for some and not for others.
At any rate, you need to make sure they always test for the biologically active thyroid hormones, Free T4 and Free T3 every time. By comparison, your latest tests for T3 Uptake and Free Thyroxine index are outdated and not very useful, but your Total T4 and TSH are indicative of hypothyroidism. So you need to keep a close watch on your levels of Free T4 and Free T3, and more importantly, be alert to any symptoms that show up.
Also, don't overlook the importance of Vitamin D and ferritin. Be sure to get those tested and supplement as needed.
Can't say that I have run into anyone with Graves' that was not confirmed with a TSI test, but was diagnosed with an ultrasound, Why was the doctor sure it was Graves', instead of postpartum thyroiditis, which you can read about in this link.
http://www.mayoclinic.org/diseases-conditions/postpartum-thyroiditis/basics/symptoms/con-20035474
Postpartum thyroiditis seems more likely, since it usually starts with a period of hyperthyroidism, then can normalize, or turn into hypothyroidism. To me, that seems more likely than the scenario of going from Graves' (hyper) to hypo, by supplements and lifestyle changes.
I agree that hyper is worse than hypo, but even short term, hypo is not what you want, and longer term it can lead to more severe problems. Best way to diagnose for hypothyroidism is by symptoms and also levels of the biologically active thyroid hormones, not by TSH. Also, most of the recent tests done for you were outdated and not very useful. You should make sure they always test for both Free T4 and Free T3. A good thyroid doctor will treat a hypothyroid patient clinically by testing and adjusting Free T4 nd Free T3 as needed to relieve symptoms, rather than based on test results.
Also, since hypo patients are so frequently deficient in Vitamin D, B12 and ferritin, you need to get those tested and then supplement as needed to optimize. D should be at lest 50 ng/mL, and B12 in the upper end of its range, and ferritin should be at least 100.
So tell us about any symptoms you are having.