I finally came across a forum that had a simple elegant answer. In the Library/Linkage you simply put the name of your class into the Base Class field instead of the Class field.
So I tried that, and I still got an error and after tinkering a bit, I realized that something also needed to be in the Class field for everything to work. If you leave the Class filed blank, you will get the same error quoted above. To fix this, just type anything into the field. When you click OK to leave the Linkage dialog, flash will warn you that the gobbldygook you typed into the Class field doesnt exist as a class - but just ignore it.
You should now be able to have multiple different symbols using the same class. Just do the above for each item in the library.