Though TDMS is the solution ,
TDMS is a licensed product and it will cost much more than adding space to your QA system . Moeover to set it up and operate it to your requirements will cost much more to your client .
Believe the only option for you is the Client copy tools ( You can exclude tables which are not relevant ) - Disadvantages may be the resulting system may not be consistent enough when compared to production .
What is your database ( Check whether compression can be enabled when using the export import method . for eg : DB2 allows you to export and while import you can choose all tables compressed )
Disadvantage - Downtime for production during Export
Thanks ,
Manu