Well, I resolved my problem, but I don’t like how I had to do it.
For reference, (as far as I can tell) the only way to add a column to a dataset that is already attached to an rdlc is to hand-edit the xml (i.e. open the rdlc with your favorite text editor and add a Field to the appropriate table). After doing this, the field appears in the Report Data pane, and I can use it as if it were there from the beginning.
I would still like to know how to perform this seemingly simple task from the UI, but nonetheless my current problem is solved.