That sounds very much like several years of my own iron deficiency problems in the past. I went that far to phase out azathioprine among other things because of iron deficiency. Turns out that aza wasn't actually really responsible for the low iron and low hemoglobin but a combination of malabsorption and just generally a chronic malfunction of low hemoglobin that starts to happen when your ferritin blood level is just constantly low. Blood transfusions are the absolute last resort (and yes I had them 3 times, always 4-5 over 2 days in hospital). My lowest measures hemoglobin level at the end of 2011 was 5.2 once... Not recommended.
Today I am at a hemoglobin level of 16.5 (last measurement a month ago) and ferritin levels above 100 despite 150mg aza per day. The reason is pretty simple a. I am in deep remission so my last diahrria was about 5-6 months ago I believe, b. I am taking 160mg iron supplements in tablet form (I searched long and hard until I found tabs that didn't upset my stomach) and 80mg of solvable tabs (using a LOT of water for dissolving the tab so it's not intense) and c. Endurance sport (in my view very important for higher hemoglobin levels). Lastly, vitamin D, B6, B12, folic acid, magnessium, zinc, potassium supplements.
P.S. you say your iron levels seem normal, do you know your current ferritin levels?