"Is there a way to do this without creating a separate database? (like making multiple layouts on a single database and restricting what data appears in each layout)"
This is what you want to do instead of moving records in and out of a second database--though there's a better way to control access than using different layouts.
Add a text field, SubmissionStatus, use a value list to store values in this field such as Pending, Active.
Now to make a newly submitted project "Active" you simply change the record's status from "Pending" to "Active". You can perform finds to pull up just those records of the status you want to see. You can use Access Privileges to restrict access to records of a given status to users who log in with a password that uses a specified privilege set. This is called "record locking" and if you click the advanced search link above and enter that phrase, you'll find several threads that discuss this method.