Thanks for your input, it helped point me in the right direction.
As it turnes out it wasn't at all that dificcult. In the IDataSourceKeyResolver implementation, where I create the ClientEdmKey with correct user credentials, I also change the SSDL reference in the connection string. I grab the original single SSDL file built with the project, creates a copy, replaces the schema name in the copy, and finally inserts a reference to the copy in the connection string.
With this solution we can dynamically add new customers and schemas to the database, update a single configuration file, and the application will automatically adapt to the new schema at logon time. We don't have to manually maintain and update multiple SSDL files.
Mikael