So sorry for your losses, it really is heartbreaking, and it's so hard not to have clear answers.
I've just had the blood tests done after two miscarriages and am awaiting the results. From what I understand, it's a good thing if they didn't pick up any issues with clotting or immune response in the tests. I feel more like I want them to find something that they can treat, just so I can feel like I am doing something.
Statistically, after three losses, your next pregnancy is still more likely to be successful than to be another loss. This is shown in the data and also in lots of stories on here. It's so hard when you left waiting and not knowing though.
I find it really confusing that the doctors don't seem to agree on Progesterone. From what I understand, there was a large scale study called the Promise Trial, which was carried out by Tommy's and leading specialists from St Mary's Hospital and it found that Progesterone did not reduce the likelihood of loss. But lots of doctors do still prescribe it and they do seem to agree that it definitely can't hurt. I don't mean to take away your hope for Progesterone, as lots of doctors still believe in it, plus there are LOTS of stories on here with people who have had successful pregnancy after loss, with Progesterone supplements (hopefully some people will share their experiences of that).
I guess the hopeful thing is that you're still more likely to have a successful pregnancy than not, even if you did nothing. But it's great that you're getting information and treatment.
I really recommend Lesley Regan's book on Miscarriage, which explains a lot of the causes and treatments. It helped me and I found it reassuring. Wishing you all the best, and I hope you get lots of support in the meantime, on here and in 'real life'.