I had LASIK surgery done a couple of years ago (monovision, like you're having). I'm not on Coumadin, but I made a point of asking about it. If you're an appropriate candidate for LASIK, my eye center had no problem with anticoagulation.
There is no bleeding anyway. The presurgical visits are long and full of tests, but the actual procedure is almost absurdly quick. The machines even compensate if you move, or stop if you move too much (and here I thought they'd have my head stapped to a board).
I've worn glasses since I was ten, and had astigmatism. My new glasses were to be trifocals with progressive lenses within the three panes. They needed instructions. That convinced me
After the OHS, I was much less concerned about "mere" eye surgery, and I went to the best (one of the pioneers). My vision worls perfectly now, and no more glasses. I still delight in it.
Best wishes,