Ferritin of 116 is perfect in my book.
Hemoglobin 13.6 g/dL for a woman is okay, while for a man would be low.
A serum iron might help you know how well your copper stores are helping to bind iron for transport to the cells. For instance, a high serum iron with a good ferritin would indicate copper needed work. You might have adequate levels of copper, but it doesn't work right if it's out of balance with zinc. Serum levels of copper and zinc work best in a ratio of copper/zinc 0.7-1.0/1.0.
Regardless, between iron and thyroid, it appears that thyroid is the more likely culprit in your hair loss.
You asked about your protocol, and I think it looks good. I wouldn't mess with it before being sure your thyroid health is being addressed optimally. I regret to say that I needed thyroid hormone after all.