This guide needs to be updated for Mint 13.
I followed the guide for Mint 13 as best I could, although libpulse* packages are now different.
I was able to get the sound applet back on the panel nicely by installing gnome-alsamixer and the package: volumeicon-alsa.
It would be nice if pulseaudio could be cleanly removed without leaving random pulse packages around. For example, if I try to remove certain libpulse packages, the package manager tries to remove at least half my system.