Thanks John. I've been looking at their site for a few minutes and it seems pretty robust. And complicated because of it.
Just added rsync to the list of requirements.
VortexBox is a Fedora-based distro that already includes SqueezeBox server and a web UI for managing shares and similar features. It doesn't include a web UI for routing, but I suppose that could just be done on the command line as I was planning to to originally with Debian. 15-20 bot times are quoted by the maintainer - that would be very nice.
Apart from that I found some router distros with two notable examples being:
Untangle:
http://www.untangle.com/routing-qosZentyal:
http://trac.zentyal.org/screenshotsNo idea how easy it would be to get SB Server on either of those.