I found a device-dependence issue here!
I have a Sony Blu-Ray BDP-S-770 and an XBox 360. When I try Amazon streaming on the Sony, it works without buffering at all, no matter when we try it. Netflix is horrendous, buffering a minute after every 45 seconds of play, at its worst. HOWEVER, I found that using the XBOX 360 for streaming Netflix, it actually works without repeated buffering, albeit at poor video quality. We tried a PC and it also worked without repeated buffering. Those of you who are really interested in the program you're watching (House of Cards, anyone?) might be able to get the plot fix if you switch to a different device.
I signed the petition above and got myself even more upset at Verizon. I pay them $30 each for data plans for 3 cell phones plus $40 a month for FiOS Internet. I also have Verizon home phone and FiOS TV and subscribe to all mainstream premium channels. Total bill per month is over $500. What else could Verizon want from me to allow me to watch Netflix?