Thanks Bruno!
While at first glance, the ability to multi-select and move would seem sufficient, the problem becomes much more complex in diagrams that contain 3 or more swimlanes. In order to move elements around, you have to move the first set out of the way. Then you have to select the second group and move that set to its new location. Then you have to move the first set into its new location. This is a three move operation that gets even worse as the number of swimlanes increases.
In the diagrams of one of our projects, it is not uncommon for the Analysts to create diagrams - typically Happy Path schematics - that have 7 or more swimlanes in various stages of completion. As demonstrated above, moving these elements around becomes an exercise in frustration, if admittedly not an impossibility. It is further complicated by the requirement that the swimlanes, which do not behave as first class diagram elements, must be reorded via the dialog - which can lead to confusion as to what moves where.
Of course, I am emphasizing the pain - since when the need to reorder occur, painful it is - in extremis.
I have bastardized the use of fork/join elements to create pseudo-swimlanes that can be grouped and moved. However, this is not a satisfactory solution.
If EA could automate this, I echo your comment: This would be GREAT!