If you were my patient, I would test for several disorders, including anticardiolipin antibody and lupus anticoagulant. In addition I would want to test for such things as Factor V Leiden, etc. Depending upon your heritage, some problems are more likely than others.
I would want to know the results of these tests because it would help me decide whether to start aspirin even before you try, and possibly heparin after conception. Your history is certainly suspicious for some type of coagulopathy. A good gynecologist or Reproductive Endocrinologist could do this type of testing for you. A Perinatologist might also be a good consultant.