Blu-rays don't do anywhere near 277Mb/s.
First, if it was 2GB * 2 for the source of your recompressed copy, that's 4GB * 8 bits per byte = 32 Gigabits (Gb), or 32,000Mb. Two hours in seconds is 60 * 60 * 2 = 7,200 seconds.
32,000 / 7,200 is 4.444Mb/s. Streaming your 2 hour long 4GB movie could be done with ~5Mbit. A 1Gb/s connection could handle streaming ~200 of these movies.
Going back to Blu-rays as a source, an Ultra HD Blu-ray maxes out at 144Mbit but in reality most movies are encoded at a much lower bitrate. Most movies will cap out around 40-50Mbit. You could do 20 of these straight Blu-ray movies on a 1Gb connection.
https://en.wikipedia.org/wiki/Ultra_HD_Blu-ray#Specification...