I had a great idea today. Why not use my old iPod touch as an AirPlay receiver, rather than a Raspberry Pi?
I installed Airfoil, but it crashed immediately on opening the app. Then I installed AirPlayServer, which seemed to work. However, the AirPlay connection from iTunes was pretty shaky and tended to crash iTunes a few times before it started working. Once it did, I hooked it up to my speaker, and the music was almost inaudible. If this is going to work, I'm going to need to boost the volume a lot.
On the plus side, I acquired a portable battery pack from BoilerMake last weekend. It's 5V 1A 2200mAh, so it should be enough to power an iPod or a Raspberry Pi Model A for a few hours. We'll see how things turn out.