Re-ordering records in a ListGrid

I have a ListGrid that is associated with a client-only data source. The user can select a record in the grid. I want to have a toolbar button to move the selected record up or down one record. However, I have not been able to find a way programmatically to move the record in the grid (the grid is not sorted).

Can you point me to how to do this?

I've tried calling getOriginalResultSet() and then using a combination of removeAt() and addAt() to move the record, but that had no visual effect on the grid.