Here is my solution. Has worked for the last 2 seasons.
Fire TV + Express VPN + MLB.TV
On Fire TV, you have offical apps for both MLB.TV and Express VPN
I pay for MLB.TV, and pay $5 a month also for Express VPN.
Before selecting a game on MLB.TV, I use the Express VPN app on my Fire TV and select a location. Usually somewhere in Europe as selecting Canada or Mexico has had shaky results.
After I've selected a location on the VPN app, I go to the MLB.TV app. Select a game and team feed (always MASN Nationals feed) and no Black Out.
I am giving MLB the money they ask for and just side stepping the blackout.
*remember to turn VPN off after game* as not doing so will often conflict with Netflix/Hulu. And that is the under the table agreement with MLB you see. MLB could easily detect and block me like the other services do, but they choose not to.