You should be able to rename files while you do pack and go. Also make sure this option is checked
Other easier way would be to set up the master assembly using DriveWorksXpress (a free design automation tool included in SOLIDWORKS since 2008 version). And then can set up the rules and a user form. Finally have your new models/drawings created on fly.
Here are some sample projects to get started: DriveWorksXpress
If this works great, then you can scale to higher version of this tool which would give more options/flexibility.
As Deepak Gupta said, you can easily rename components as part of the Pack and Go process and they'll maintain the references. Double-click on the file name in the column indicated below to do that. Another option might be to assign a distinct project number as part of each file name for each project, then use the Save/Replace button to search all file names and replace one group of numerals or letters with another group instead of renaming them individually.
Deepak and Glenn, thank you for the insights. I will try these out today and explore the DriveWorksXpress app. - G
I have taken a look at your assembly for a few minutes and noticed your have no in context relations. What I mean is that you did not build this in-context with the rest of the components, in which would help changing a few dimensions to update the size and the rest of the components. Drive works express will work as well.
For instance the way you created A11202 should be created on Plane 2. Modeling this in a different would help accomplish what you are try to do.