FWIW -- I'm not suggesting that you do anything other than try to navigate your insurance maze. People on the forum have commented on how Alere or other services have been helpful - and the cost per test (after insurance pays) is about $6. This isn't too bad, if you can make it work. This is not much more than the strips cost.
I'm a self-tester, not insured, carrying all the cost on my own. There's a bit of freedom involved - if my INR changes due to changes in diet, dehydration due to heat and too much work, or whatever, I'm free to test more often than a lab may recommend or insurance may reimburse. I can make minor dosing adjustments and see if there's a change in three days, and, overall, have the freedom to monitor and manage my own anticoagulation. Not everyone can or should do this themselves -- I'm assuming that most on this thread already can and do.
Even if it's just a matter of doing the test and reporting results to your doctor, having your own meter gives you the freedom from drives to the doctor's office, some of the fees, etc.
I bought my own meters (yes, more than one meter) on eBay. My first was a ProTime, and I upgraded to a ProTime 3 (for about $50). Both machines work fine for me, and the quality controls built into the strips help reinforce my confidence in the accuracy of the test. I also now have a CoaguChek S - bought brand new, in the box, for well under $100. These last generation testers are, in many cases, quite affordable on eBay. The strips may be a bit of a challenge - but you should be able to get them for less than $6 a strip.
NOTE: I just learned that no strips will be available for the CoaguChek S after October 2011 -- this is a meter that should probably be avoided because of unavailability of strips.
If your insurance company won't work with you on reimbursing for a purchase of a meter, you MIGHT consider buying your own on eBay (or some other source). I was able to get my CoaguChek strips on eBay, from a dealer that I sensed was trustworthy (buying things like this on eBay may be a bit of a risk, especially if the strips are supposed to be kept refrigerated). The strips arrived in a few days and were fine. I ordered my ProTime strips from a medical supplier who I thought was keeping them refrigerated and would ship in a cold pack. They may have been refrigerated at the warehouse, but were shipped without cold pack and arrived overnight, sitting all day in a hot UPS truck. They survived the trip. If you buy from a medical supplier, you'll probably have a better experience, and your insurance MIGHT pay for strips and not meter.
My point here is that if you hit a stone wall in dealing with your insurance company, you're not out of options if you still want to self-test.