SQL Server Backup – How to Backup and Restore Part of a Database

I don't know of anyway to do a schema backup or restore in SQL Server. Your solution of putting all of the schema data on a filegroup will allow you to restore the database to another server, but will require that you restore the primary filegroup as well. (note, this is possible on SQL Server Enterprise Edition versions 2005 and above). One problem for your situation might be that you could only have one of the partially restored databases running on the same instance of SQL Serve This link covers the piecemeal restore process: http://msdn.microsoft.com/en-us/library/ms177425.aspx

In short, no, you can't backup the individual files that you want to restore. According to BOL, the only way to backup files on a database that uses simple recovery model is if they are all backed up up together: http://msdn.microsoft.com/en-us/library/ms179401.aspx .
Have you considered differential backups of the files? Doing this would give you smaller file size for backups (still requires a full at some point), but would also increase the number of steps required to restore the database. Differentials partial backups are described here: http://msdn.microsoft.com/en-us/library/ms190218.aspx.