Even though the medical world treats Hashimoto as if it was the same as just regular hypothyroidism, it really isn't the same as just having a slugglish thryoid.
The antibodies rear and confuse the whole endocrine system with hormones. In many cases the TSH can remain normal ( in many patients) but the antibodies are messing with other things causing a world-wind of issues for the patient.
Antibodies are a direct attack on the immune system trying to break that down to make the patient sick. They also (depending on the type of antibody like in Hashimoto) will send an evil army of TPOabs to the thyroid to directly hit that too. Combat on both ends - thyroid and the immune system is needed to suppress to lower the TPOab antibodies to stop attacking both areas. That is why selenium and other things are speculated to help and sometimes can - depending on what truly you are lacking to allow the antibodies into the immune system.
Selenium is not a thyroid enhancer. It is an immune builder to fight off sickness. A few major things connected to the immune system can be low Vit D, Low Vit C ( hense adrenal fatigue + immune) Vit B, zinc, copper,magnesium and iodine. The hard minerals - especially iodine - are tricky to trial due to rearing healthy tissue and then essentially making the antibodies more angry on thr attack of the thyroid causing more attacks to go on.
Look how low you are on the Vit D tests. That in itself could be the essential issue causing the antibodies rage and you could certainly benefit from a supplement involved with Vit D-3 to see if that helps out.
Google up Vit D and Hashimoto disease and read the articles on how adding in D can help. That was the only thing that permanently lowered my counts but I was on high levels of D in the range of 15000ius daily - and still take that dosage too.
http://www.goodhormonehealth.com/VitaminD.pdf
http://www.medhelp.org/posts/Thyroid-Disorders/Hashimotos-Vitamin-Deficiencies/show/362449
http://www.medhelp.org/health_pages/Weight-Loss/Dietary-Supplement-Fact-Sheet-Vitamin-D--Page-1-of-3/show/1005?cid=129
http://doctorbrady.wordpress.com/category/hashimotos-thyroiditis/
http://www.vitamindcouncil.org/vdds.shtml
just a few article... LOL - I have more ;)