Is it not possible to define a base node within the "rotate" window?
If I want to set the origin as my base node, but I don't have a pre-existing node defined at the origin, do I have to abort the operation, exit the tool, create a temp node at the origin, restart the "rotate" operation, and then select the temp node that I just created as a base node?

Yes I believe you would need to create another node to reference as the base node for the "Transformation Tool". If you don't need the advanced features of the "Transformation Tool", you could alternatively use the "Move" tool: