Where would I be able to set the directory options that are available in the Save Preset dialog? I checked the documentation for the dialog and it says there should be three options for directories to save to, $HIP, $HOME/houdinix.x, or $HFS/houdini | $HFS/bin.

However in our studio env I'm not seeing any of those options, but instead I am given the option of $HOUDINI_USER_PREFS_DIR and nothing else. This makes me think the available directories can be changed or set, but I can't find anything in the documentation…

They can only be saved in directories with which the user has write permissions. In a studio that usually means only the user prefs dir, but any other writable location in the houdini path should work.

Yup that makes sense, just tested and that does seem to be the case, any path in HOUDINI_PATH that the user has write permissions for, and you can save them there.