But hey, they can play back video pretty OK, so I eventually settled on a mix of video and live streaming a desktop browser rendered on a normal PC:
http://the.taoofmac.com/space/hw/RaspberryPi/Streaming
Thing is, omxplayer crashes out of the blue for no apparent reason (either halts the player process or locks up the RPi _completely_, on any hardware rev) and have an alarming tendency to corrupt SD cards, so I'm moving to the Beaglebone Black ASAP.
They do make very nice low-power servers (I have one doing AirPrint via CUPS for iOS devices), though, and of course I try out a bunch of things on mine - if it runs quickly enough on a Pi, then it's blisteringly fast on a "normal" machine.