Thank you, Abegail.  I'm not seeing a way to link a new account in Chart of Accounts to the main project account as you suggested.  Did you mean to say to ensure to link it to the parent account in the Chart of Accounts?

The whole point in wanting subprojects is to be able to bill customers as each subproject is completed.  Since you mentioned "help organize your projects without billing them directly to clients", I don't think this is a viable option for us.