Well crap. That didn't work. Here's the breakdown.
Wired ethernet cable from Airport extreme (firmware 7.6.1) to Apple TV (Firmware 5.01)
I double checked to make sure it was using the wired connection (go to wireless and it says can't use until you unplug the ethernet cable, so it was using the right connection.)
Watching netflix, not 15 minutes into watching the same movie we tried watching the night before, it drops and restarts again. Gah! Apple, what the heck guys?
Since the wired ethernet cable didn't work, I'll assume neither will the powerline.
I think that's the last idea to try, right? Anything else?