I tried Erica Sadun's AirPlayer, a Python script that, as it turns out, implements version 2 of the AirPlay protocol -- the one that supports video and images. What it DOESN'T support is sound, at least not without the appropriate crypto key.
Which led me to Shairport, vessel of the secret sound-support sauce. Shairport only implements AirPlay v1, which can't handle images of any kind. Which means that the video portion of YouTube can be streamed from my iPhone to AirPlayer, and the audio portion to Shairport, but I have to choose one. Huzaah.
This worked well enough for iTunes, but iOS, ie, my iPhone, didn't work until I disabled IPv6 on my Linux box.
