Revit :: Family Type Parameter Breaks Constraints?

I am creating a family for a mobile shelf assembly.  While an obvious way to create it would be to use an array, because the client needs to be able to tag each shelf unit separately, that can't be done.  The client does, however, have a limit of 10 banks maximum, so I've created ten banks in hte family that are controlled by visibility parameters.
 
Each of the banks can be a different type of shelf (the shelf units are nested families) but they are always of the same overall length and width in any one run.
 
Here's my problem, Everything flexes correctly as long as the depth of the units stays the same as they were when the family type parameters were assigned to the shelf families as labels.  When you try to create a new Type using a wider shelf unit, you get errors.
 
Without the Family Type parameters assigned as labels, all of the reference planes meant to drive the location of the shelves flex correctly.
 
I'm using Revit 2013.