A few things -- this may get a bit lenghty, so please bear with me.
It's been nearly 20 years since my AVR. I don't recall much extra effort being done by my cardiologist to get me to a good INR in the weeks post-op. It's possible that I may have had blood draws more often than once a week initially, but this may be an unpleasant memory that my mind has blanked out. I DID have a cardio who wanted me to have my INR tested every two weeks -- he even wrote an open prescription to have the test done.
In your case -- if you're still pretty short term post-op, as others have noted, your INR will probably fluctuate. I'm concerned by your statement about now getting your blood tested EVERY TWO WEEKS. Taking a massive dose like the one you're taking (105 mg/week!) is pretty scary, and if your body should heal to a point where a much smaller dose is needed, you may be heading to a dangerously high INR with such a high dosage - whether or not you're completely vegetarian. With a dose that high, I'd be much more comfortable testing once a week - or even more often - just to make sure that my INR doesn't spike. I'd be watching my body for any signs of bleeding or bruising. I'd like to be pretty certain that I don't wind up suddenly highly overcoagulated.
For the past two years, I've had my own meter(s). I've been able to test as frequently as I thought I needed to. Currently, I test once a week. If I was taking a large dose of warfarin, or made major diet or dosage changes, I would probably test more often. I don't go crazy about testing too frequently - but I want to know what's happening with my body because I don't want to make my wife a widow or custodian to a vegetable.
Even though some insurance companies claim they won't pay for you to do self-testing until you've been on warfarin for 90 days (or something like that), during this period when you're healing and also trying to find the right dose, I think it's important to monitor yourself for any signs of overcoagulation (the bruising I mentioned, plus bloody stool or urine, spontaneous nose bleeds, or other nice things like that) and be able to tell your doctor or clinic RIGHT AWAY. I don't think you're being handled properly if a) your INR hasn't stabilized because you're still healing, b) you're taking what for most of us would be a massive dose two or three times what we normally use, and c) you're only being tested every two weeks.
Being on veggies is good -- the high levels of Vitamin K in your system should make it easier to manage your INR once your body is again stabilized. Vitamin K has other benefits beyond those relating to coagulation. I'm not sure that green things - no matter how much - can make such a drastic change in usual warfarin dosing as requiring what would be double what some of us take.
What I'm suggesting is this: 1) If you can, get yourself a meter. Having a meter is empowering. Having a meter means that you're not having to deal with a blood draw (just a finger stick), and that you're not dealing with a phlebotomist who probably couldn't find a vein if it jumped out of your skin and said 'here I am.' Having a meter means you can test more frequently than your clinic asks you to -- if you think there's a reason for more frequent testing. It could save you a trip to the lab - or the O.R. 2) Talk to your doctor/clinic and suggest that, while you're on such a high dose, it would make sense to test a bit more frequently just to verify that your INR might not increase once your body heals and no longer needs so much anticoagulation.
I think we've all taking this ACT ride. I'm just concerned with your dosing and testing frequency. I hope it all works out well for you.