Hi Daisy, sorry to hear about your difficulties and losses. I too have a (albeit now treated) underactive thyroid issue and the rest of them are right - there is a lot of research to indicate that TSH needs to ideally be around 2 or less for conception.
I am hesitant about what I am about to write here (as I am really not a doctor and will not go around diagnosing people!) but I will tell you my story in case it rings any bells.
I was diagnosed with an underactive thyroid age 20 and have managed to more or less balance it over the years. I find I work better at a TSH of around 1.
After having a third miscarriage last year I lingered a lot on the Recurrent MC thread that NappyMaestro mentions above. It was that which first lead me to start researching immune issues. I have always had raised thyroid antibodies (indicative of Hashimotos) and there are theories that say this goes hand in hand with something called High Natural Killer Cells - where the body can kill off a pregnancy at an early stage (sometimes pre-implantation, sometimes as a miscarriage) as a 'foreign object'. It often goes hand in hand with a family history of thyroid, allergies and other autoimmune conditions. The TTC on Prednisolone thread is where myself and other immunotherapy patients hang out. Prednisolone is the steroid we have been on to stop the body fighting off the baby. Feel free to come on over and ask anything!
The doctor most of us are seeing can be found by googling the Miscarriage Clinic. Also worth reading is Dr Beer's Is Your Body Baby Friendly. I will say that these theories are contested by a lot of mainstream medicine so not everyone believes in this.
I am also in no way implying that this applies to you, but after I had had similar issues for some reason it just rung a few bells that this could be my issue - and a visit to the Miscarriage Clinic did indeed diagnose me with very high NK Cells. After one blighted ovum on the treatment and a bit of treatment adjusting I am now 22 weeks pregnant. I am in no means home and dry but, for my fifth pregnancy, it is a good start.
Hope that helps in some way. Even if it's just something you can rule out.