Thanks, mjolinor... put me on the right path.
MyInvocation.InvocationName
gives you the name of the command that the cmdlet was invoked under, but the calling script name is right close by...
I found what I was looking for here (from within the PSCmdlet-derived class):
var callingScript = MyInvocation.ScriptName;
It contains the full path of the script that called the cmdlet.