Geo-restricted streaming service content is nothing new. Sometimes you can skirt these restrictions with a VPN, but often it doesn't work the way you want because your account is pinned to a specific region. The streaming company knows you're not jumping back and forth from New York to London multiple times a night.
There is one workaround worth trying, though: change the DNS settings on your Fire TV Stick sostreaming companies can't block what you're watching. Unfortunately, to no one's surprise, it didn't magically remove any content restrictions in the Netflix app on my TV. However, changing the DNS settings did something I didn't really expect, and in a good way.
Meddling with the DNS settings somehow improved the network stability on my Fire TV Stick. In hindsight, I think I'd rather have better network stability and speed than a few new movies to binge on Netflix.