Figured it out -
Expand Sites, <YourSite>, right click Parcels, select Properties. In Site Parcel Properties dialog, Composition tab, middle right, change User-defined property classification drop down accordingly for your UDP's class (i.e., Unclassified, <YourCustomClassName>, etc.), and hit OK Button.
Now your UPD can be included in the 'table' view of Toolspace.
I was incorrect that I'd done all of the prerequisites for UDP, because I was able to assign a value to individual Parcels (via right click Parcel Properties dialog).