First, I would look for a dentist who will replace the amalgam filling with a ceramic casting - my dentist did that (some years ago) with several old, very large amalgam fillings. Problem solved. Amalgam never quite becomes fully hard, so as you bite down on it, it spreads the force of the bite outward, eventually cracking the tooth. Ceramic castings are solid, and glued in to the remaining tooth structure, so they don't realign the forces of biting outward.
Second, if the first isn't going to happen (root canal costs more than ceramic - it isn't really worth waiting), if you take an antibiotic, do not take a one-time bolus (premedication dose). It has not been proven to prevent infectious endocarditis. If you are going to bother to take an antibiotic, ask for a full antibiotic course, starting the morning of the dental work.
As far as bleeding, there are no known cases where anyone on Coumadin (warfarin) has bled to death due to dental work. There are cases of people going off their Coumadin and having strokes: so don't. You can work out getting to the lower end of your safe INR zone.
There have been some cases where people had to go to a hospital eventually to get the bleeding to stop, but that is quite rare. For almost everyone, it's not a big beal.
Best wishes,