Others have reported Netflix blocking IP ranges owned by cloud hosting companies. So this solution might not work. What if it was a peer-to-peer service? Whereby the ultimate exit point was the home internet connection of another subscriber?
Maybe if there were some way to break the stream up into individual media files, and then you could download one identical file from lots of different users at the same time.
https://en.wikipedia.org/wiki/Multipath_TCP
but that requires the cooperation of Netflix, naturally.