You might want to think about taking a different approach altogether...cheat
Create two worksheets that are essentially the same except that one is uses you grouped dimension, the other doesn't.
Use a parameter to show/hide one or the other in the same real estate on your dashboard. You can find an example of how to do that here: http://www.alansmitheepresents.org/2011/03/changing-viz-types-with-dashboard.html
I do not mean to steal your post. Alas, I have an extremely related question which may or may not help Stuart. If you were to create a "grouping" using a calculated field with a case statement, you would be able to select between those fields using a single graph and a single parameter. However, if you were to use Tableau's "Create Group" feature, you cannot use this group in a calculated field. Why is this?
This is as designed. However, in Tableau 8.0, a set can be created and used in a calculated field (this does not work with JET--so take an extract).