Add a database role to the add database set up
When you add a server could you create an SQL Account for the application to use? This would assign the basic minimum permissions that are needed. This should be fairly easy as the set up has to be done by someone with sysadmin to the server. The details could be stored in the RedGate database, against the server with the password encrypted or hashed.
Then when you add a database it could create a role and add the application account to the role as part of the setup to make it quicker.
This would streamline the setup procedure, but you could provide customisable scripts if user prefer.