Sara, those are brilliant betas!
I am Factor V Leiden heterozygous but with a history of clots (which is why I have been anticoagulated for so long.
I don't know whether you have read the guidelines but they are here:
www.rcog.org.uk/womens-health/clinical-guidance/reducing-risk-of-thrombosis-greentop37a
From page 20 onwards is probably most interesting for you as it explains the heparin dosage.
There is also a separate guideline on management for recurrent pregnancy loss, which you can access from the same website.
The guideline I linked you to is for clot prevention but I think it is appropriate due to your homozygous thrombophilia.
Your doc seems quite proactive with the heparin dose. Either because he considers you high risk/just wants to be careful or because you are overweight, in which case the dose is increased. You might be on a higher dose than most ladies here but it is not excessive. For instance, if you were now diagnosed with a current clot you would be treated on an even higher dose.
The one thing that does seem a little unusual is taking shots three times a day. To space them out evenly would mean taking one every 8 hours which seems a little inconvenient at the least. Your doc might have a special reason but in a general case I have never come across this. You might want to take your doc up on the offer of one lower and one higher dose a day.
To be honest, from what I see nothing suggests you HAVE to be on heparin so why go completely overboard?
As for the prothrombin test, Dr google suggests that low molecular weight heparin (clexane is of this type) does not always prolong the time, which is why an anti-Xa assay might be more effective as a test. This is all quite complicated stuff, tbh, so I don't want to say your doctor is wrong! In any case, as I mentioned before, your higher dose may be unusual for rpl ladies but not unusual as a dose administered during pregnancy.
As for the aspirin, that is a whole different discussion. I would want to take (in fact, I do) but your doctor needs to be on board as it can affect your blood results. Any chance you could bring it up again, mentioning the elevated risks of recurrent pregnancy loss, IUGR, preeclampsia and clots at the placenta linked to thrombophilia?
Sorry, I am not sure whether the above is clear. It doesn't help that I am typing on my phone and have a cat cradled in one arm

Do feel free to ask me further questions.