SSRS + MDX: Dynamic Dimension Attribute on Row Axis

Earlier this year, while building an SSRS report against a Cube data source, I got stuck trying to parameterize the dimension attribute on the rows axis of the dataset query. What I wanted was to provide the user with the ability to select the dimension (via an SSRS parameter) along which to calculate the measure.

My initial attempt consisted of building a dynamic MDX query and using a query-scoped named set and simply substituting in the dimension-parameter value at run time.