Hi Fluttershy,
You may have a couple of options. Since you are over 18, and presumably have access to health insurance or subsidized health care, I would recommend you see a therapist who is knowledgable about gender-related issues. He or she could presumably write a letter to the endocrinologist after a few sessions.
If that isn't quick enough for you, you could see if there is an LGBT center near you that can prescribe hormones on an informed consent basis. In either case, you should continue to see a therapist, even if you feel like you don't need one. Transition is hard, and you should always try to have some form of support in place, be it professional or your friends, before you start.
Anti-androgens such as spironolactone or cyproterone acetate (CPA) do not cause cancer. Spironolactone has been used by millions of patients over the last 50 years and is safe and effective as a diuretic (its intended use) and as an anti-androgen. CPA is not available in the US; there is some concern over hepatotoxicity (liver damage).
Finasteride is well tolerated by most individuals. The most significant side effect is loss or reduction of male sexual performance. For most transgirls, this is not an issue. Spiro and CPA cause this as well, so it really is part and parcel of hormone therapy. The other possible side effect is depression, but that is fairly rare. I have been using finasteride for about ten months now, and have seen regrowth of hair at my hairline, where male pattern baldness really took a toll. I think you're endocrinologist is not taking you seriously. If you can get a letter of referral from a therapist, that may help.
With kindness,
Terri