At a glance, the iron panel isn't all that bad ... If you brought your iron serum up about another 25 to 40 points, it would be just about optimal for thyroid hormone purposes, with getting hormone transported to the cells. However, as you have already broached upon, cortisol and the adrenals will play a strong role with thyroid productivity, as will other variables.
Without speculating too much, it would be good to see a complete thyroid panel (TSH, FT3, FT4, RT3 & TPO & TgAb antibodies), and if you by chance were to have a 4x saliva cortisol panel, that would provide A LOT of insight. A metabolic profile with electrolytes would also be helpful, and even D3 can be beneficial in this discussion.
Also, just for future reference, your Saturation % is simply a calculation of Iron/TIBC (transferrin), 100/422 =.2369. In the labs that you mentioned that were from March (TIBC was 540, Saturation was 11%), so reverse calculating this would indicate that your iron serum at that time was at/around 60? When iron is deficient, it's 'normal' to see both TIBC and UIBC on the high side, which again will calculate a low saturation %. Sometimes other metabolic factors/disease can influence these figures, e.g., hemochromatosis (which is in my family), which would/should prompt other labs & exams.