I am always reluctant to see a person get on a life time of thyroid medications when the root cause might be a simple case of iodine deficiency.
Iodized salt in prepared foods or restaurants is probably very low. So you missed out there.
Avoiding dairy means no iodine from that and also missing Vit-D3, calcium and magnesium.
Vein problems in your testes does not explain why LH/FSH is low. You appear to have secondary hypogonadism and that is not explained by high E2 or high prolactin and thus not correctable by lowering those.
Vit-D3 5,000iu per day
- others you planned, Multi-vit should provide B vitamins
Serum iron is not something that calls for iron supplements. Also need to look at RBC, hematocrit [relative to T levels], hemoglobin and ferritin. Serum iron can lead to false lows and false highs. We like to see Ferritin=80 ng/DL and you are there. That number is thought to support T4–>T3 conversion.
So you need to reconsider some parts of your plan.
Lab testes for iodine, selenium and zinc can pay for the supplements you probably need to take anyways.
I think that you are suffering from that diet and probably in ways that are not addressed in this thread. You probably also need natural source Vit-E, Vit-C, fish oil caps, other antioxidants. You can focus on learning about supplements to back fill problems with your current diet.