I went ahead and set up a dedicated shoutcast user, but it didn't help. It turns out the problem is that despite the following at the top of sc_serv.conf:
; NOTE: for any relative paths specified are relative to
; sc_serv and not to where the conf file is being stored
...the paths actually are relative to the cwd at the time the server is started. So it works fine if I cd to the parent of the logs directory before running
su -m scuser -c '/usr/local/shoutcast/sc_serv /usr/local/shoutcast/sc_serv.conf >& /dev/null &'
(or whatever), but if I'm somewhere else, say, in /usr/local/rc.d, it says "logger could not open file ./logs/sc_serv.log".