vivekd - with all due respect, I think you may be overdoing it with the Lovenox any time your INR drops below 2. If you test your INR twice a week (this is what it sounds like), your INR probably wouldn't have been below 2 for more than three days or so. Increasing your dose after the low INR reading should raise the INR in about 3 days. I don't think your risk justifies the use of Lovenox (although, I guess, it can't hurt).
According to what I've read, though, it takes about a week or longer with an INR below 2 for a clot to form on the valve. I guess, as you said, it's better to be safe, but I'm still not sure the Lovenox is appropriate for the few days your INR is only slightly below 2.
(I had an INR of 1.1 a few years ago -- I DID go the Lovenox route back then, but tested daily and after a day of increased dose of warfarin, my INR was again in safe range. )