Can you remove the NTAUTHORITY\NETWORK SERVICE group from logins and add other global user groups that you would be able to assign more granular permissions to based on the requirements...

Here is an example of the sp_attach_db syntax from the SQL BOL.

EXEC sp_attach_db @dbname = N'pubs',    @filename1 = N'c:\Program Files\Microsoft SQL Server\MSSQL\Data\pubs.mdf',   ...