Try taking the iron pills with a spoonful or two of applesauce instead of the orange juice and try using an acid free vitamin C...
It does need to be taken 4 hours from, both the levo and liothyronine, but since liothyronine doesn't have to be taken on an empty stomach, like levo, if you can't take it a full 4 hours, just give it a couple hours, if you can...
Are you splitting the liothyronine into 2 doses each day?
I have heavy periods also. Ended up needing a blood transfusion. It was tough to take iron 3x a day. Maybe a different type of iron would be better?
I did for a few weeks, but 2x was easier. Now I just do it 1x daily, with Vitamin C, orange juice with a teaspoon of apple cider vinegar and L-lysine capsule.
(Lysine is supposed to assist raising iron and the apple cider vinegar (organic unfiltered with the 'Mother') helps with absorption/digestion.
The iron makes me nauseous. I take Ferrous Sulfate.
I also take 1 tablespoon organic blackstrap molasses (high iron content) 5x a week (with 500mg chewable vitamin C). I cook in a lack cast iron pan (gives food a higher iron content)