So sorry, OP. That is heartbreaking for you both!
I am on my fourth pregnancy, with three unsuccessful ones and no living children either, also late thirties. I have been in your shoes with having seen a heartbeat and then losing it again. I am now on clexane, aspirin, and progesterone (as well as prenatal vits). Almost at the end of first trimester now, but I will not feel safe, until I hold a baby in my arms!
Sadly, my experience has also been that I am the one needing to come with suggestions for further research and medication to the NHS staff (not just NHS, btw, my SIL struggling with fertility in continental Europe has the same experience there). The staff usually then seem happy enough to go along with it, but won't initiate/suggest things themselves.
Have you tried giving Tommy's a call, to discuss your situation? They gave me some good advice, including informing me of a research center of relevance to my specific issues, and offering to make the connection. So hope things will work out for you!!
If I were you, I would start looking into the rarer explanations, as your medication already seem to cover a considerable number of the usual suspects. I think some of the suggestions above on killer cells and uterine issues sound promising as venues to look into. (Very much not a HC professional, so this is just a random's opinion.)