Do you actually have Factor V Leiden deficiency? It's not clear from your post that you do. Simply because it runs in your family doesn't mean you have it. You really should go to a doctor, because the injectable T may not even be contraindicated for you in such a case.
Now, this isn't medical advice, because I don't know enough about testosterone HRT as I'm in the opposite boat, but testosterone doesn't usually increase one's risk of thrombosis. It does increase your risk for polycythemia, which is basically having too many red blood cells. Additionally, the bleeding disorder you're worried about is actually in the opposite direction from the Factor V Leiden deficiency-- testosterone can actually cause increased risk of hemorrhage, especially when coupled with anticoagulants. In other words, testosterone can cause one's blood to not clot as well.
Factor V Leiden is a hyper-coaguability disorder, meaning that your blood will clot more readily. Because estrogen tends to increase risk of venous thrombosis, this is why you shouldn't take an estrogen based contraceptive. It would compound the risk of a blood clot that you may already have.
I hope this helps you out. And you really should talk to a doctor.