Thanks for your post!
I received a tissue aortic valve, and therefore I'm not on coumadin. My cardiologist said there was no reason I couldn't resume skydiving (I stopped when my valve stenosis was discovered 5 years ago).
People with mechanical valves have to be on coumadin, and one member with a mechanical recounted his experience with the FAA in seeking to regain his private pilots license after the replacement. He had to provide a record of his INR (blood clotting) readings for a year before they accepted that the coumadin wasn't an issue. We've also had firefighters who were unable to resume their jobs due to coumadin. If they have a tissue valve implanted (no coumadin) they can continue in their profession.
The decision to go with a mechanical or a tissue valve generally revolves around how much the coumadin restricts your lifestyle. I have always thought that a new skydiving student, on coumadin, would be more prone to bleeding incidents. I broke my ankle on my first jump and had alot of soft tissue swelling. I hate to think how bad it would have been if I'd been on coumadin.