Hi OP,
I'm very sorry to hear about your losses.
I've 'only' experienced two losses consecutively, both after seeing heartbeats too, but I then also went private and am now 34 weeks pregnant and on a cocktail of meds - clexane, pred, cyclogest/lubion, levothyroxine, aspirin, vitamin D. This was all just given as a precaution as I feel pregnant before any actual tests could be done.
I did also have immunoglobulin IV's for natural killer cell treatment as I did the 'Chicago' tests as they're so-called and had elevated levels. I had around 4 rounds of these IV's and they're hugely expensive but maybe they helped, who knows?!
You can get a uterine biopsy done for NK cells in Coventry with Professor Quenby - I know other ladies on here who've done this who've had recurrent MCs and perhaps this may be of help to you to get answers.
There was a lot of helpful info on the threads here that I just read and made notes. If you search for it, there's also a thread of ladies who are being treated by Mr Shehata, another specialist in the field of MC. I believe the thread is called the Pred Thread or something similar.
I presume your other half has had tests including DNA fragmentation of sperm?
Looking for answers is always so terrible when there seem to be none, at least no obvious ones. It's worth as a PP said to talk to specialists including Professor Reagan or Professor Quenby.