When you hold down the ⌥-key while launching GarageBand, it will open a File Chooser dialog and not open the last project. But for some reason, it will take longer to launch this way than simply letting it first open the wrong project.
Or you could open the project that you want by double-clicking it in the Finder.
Added: Holding down the alt/options key while clickin the GarageBAnd icon will first open GarageBand without showing the application window. You get simply the main menu bar and can go directly to the "File > Open" menu:
With GarageBand open you can go to then hover over File > Open Recent then click Clear Menu. Close GarageBand. When you reopen it you will get the project menu. I, too was looking for a way to open GB without reopening a past project. It isn't as ideal as disabling the option but it is a work around.