Hi!The previous replies seem to have covered everything I would have written.
It sounds like your surgeon had many meetings with the companies that sell bovine tissue valves. They probably sell the surgeon on the nightmares of warfarin therapy. Their claims are extreme, and pretty much BS if the person on Warfarin has dosing well managed (or self-managed). These claims are for people whose INRs drop near 1.0 for weeks at a time, or for INRs that are above 8 or so. This doesn't happen to people who are properly managed (or, perhaps, experience liver failure).
Self-testing is NOT particularly expensive. True, you need a meter (and some insurance may provide it, or you can probably get one on eBay), and strips are around $5 each. You may waste a few strips if you use a CoaguChek XS until you learn how to run a successful test; you may also waste some strips if you use the Coag-Sense and don't get a large enough drop of blood.
But, for around $250 or so a year, this is probably less than a latte or two each week - and can help you avoid these ridiculous things spouted by your surgeon.
Ultimately, of course, the choice between tissue and mechanical should be all yours (unless your surgeon makes a decision DURING surgery to implant one or the other).
As others have said, warfarin is practically a non-issue. (And, yes, NSAIDs are not a great idea - especially if you take too many for too long). For me, at year 28, warfarin hasn't been an issue.
Good luck making your decision. I hope your surgeon respects it -- whatever it may be.