Good luck incomplete with the tests I think they are all worth doing.

I was diagnosed with coeliac a year ago and have since learned that when untreated it may cause infertility and m/c. You would have to go gluten-free for a while for the body and antibodies to normalise, but apparently fertility can be restored on a GF diet. I also found that my undiagnosed coeliac was a deep root of my elevated TSH which was slowing down my thyroid function.

Lupus (or anti-nuclear antibodies - same thing) is a good test to get.

There are also natural killer cells tests I think that I perosnally haven't had done but might be worth considering if your are at it and getting the bloods done.

Good luck you are doing the right thing investigating this!