You know, I don't know a lot about how the whole clotting/pill thing works- but it seems to me that the hormones in the pill enhance whatever clot-causing factor that is effecting you.
When I first started taking the pill years ago, I was a smoker, and I got a stern 'talking to' about it, and the risks smokers have with clots and the pill- enough so that it was almost a contraindication- a reason not to take it.
Since you know that MTHFR is a risk for you, and that strokes run in your family, it would probably be wise to talk with your doctor about how you should manage your long term health in light of your clotting disorder. Here's a site on thrombophilias : http://www.fvleiden.org/
an article on mthfr (it's relation to homocystene levels and folate)
Allie 5-13-98 (35 weeks-pre-e)
Baby Camille 4-17-03 (36 weeks- htn and oligo)