OK folks, some interesting developments. While testing a client's server that was affected by this issue, I grabbed a precompiled copy of ices from one of our Debian Squeeze servers, copied it to the affected server, and reconfigured Centova Cast to use it instead of the copy that had been built on the CentOS 6.3 machine.
I've been monitoring the server for about an hour now, and not a single defunct process has shown up. (Previously, they'd pop up every few minutes.)
Given that ices binaries compiled using the buildices.sh script provide custom versions of all of their own non-system libraries (vorbis, shout, lame, xml, etc.) and do not depend on anything from the CentOS repos, my best guess at this point is that this is some kind of issue with the build toolchain used by CentOS 6.3.
I realize that that in itself doesn't help much for those of you experiencing this issue, but at least it's a step toward a diagnosis -- and confirmation that the problem is definitely not within the Centova Cast code base.