How can I mount a network share on a schedule?
Believe I have solved this on my own.  The part that wasn't working for me, was that Automator would always prompt me to select the specific share/folder I wanted to mount.  Turns out I missed the obvious - specify the folder in the path provided in an Applescript!  Like so:

tell application "Finder"
    if not (disk "FolderName" exists) then
        mount volume "afp://MyMac.local/FolderName"
    end if
end tell


Now I'm just going to put a few-minutes pause before this command, and set the resulting Automator app to run at startup.  If both machines unmount the remote volumes and reboot at the same time each night, all should be well with the world.  In order to schedule the execution of my automator commands, I'm just using the Calendar's ability to launch a file on alert.