I can empathize as I was in the same predicament at one point. I started with Roche Coaguchek Patient Services and found out with my first claim that it was deemed an out of network provider even though they had verified my insurance and told me the network coverage rates. I sought help from insurance customer service and was given the useless list of 'durable medical equipment' suppliers in my area. From my searches at the time, the handful of home INR service providers I found operated nationally, and it seems the trend has been consolidation toward fewer providers. My out of network predicament was resolved when RCPS was bought by Biotel. Biotel was subsequently bought by Philips.
My insurance is a self-funded plan through my employer that is administered by Anthem. I note that as a caveat in case there are different provisions among different Anthem BCBS plans, but perhaps there is some alignment in network providers. My provider is Philips Remote INR by Biotel which was in network. However, their billing switched to Cardionet (i.e. subsidiary in same company but with a different NPI provider code), and fortunately the Cardionet NPI is still in network for my plan.
US claim filing is for every 4 tests reported per procedure code G0249. The prescription from your doctor to begin service outlines a frequency range such as 2 to 4 times per month. In practice, this constrains US insurance-covered home INR testing to at least every two weeks but no more than once weekly as stated in G0249 guidance. I don't know how they would handle two consecutive claims filed less than 4 weeks apart.
At some point I decided to purchase my own meter and test strips through ebay so that I rely on a combination of home INR reporting to my doctor/clinic via the provider and unreported personal meter results. Thus, I 'informally self-manage' to my target INR with more freedom in how frequently I test.