As far as I can tell, Songbird is just a media player - it is not a server (please correct me if I am wrong in that). So, either you need to work to have Songbird adapted to include server functionality - I assume a big job - or try running Firefly as your server instead of iTunes. Firefly is a nice light-weight server which runs very well on multiple platforms.
Here is a link for a very stable release that you could try.
http://nightlies.fireflymediaserver.org ... n=svn-1586
Roku M1000, M1001, M2000, R1000, Roberts WM-201, Stream 83i