I'm glad to hear that you have ben able to resolve your original problem. Thank you for letting me know.
When opening a gallery in JuiceboxBuilder, there is no special project file to look for.
Just navigate towards and select the gallery folder itself (in your case the 'publish' folder), not a file within the gallery folder.
The gallery folder must contain the gallery's configuration file which must be named 'config.xml' (this is what JuiceboxBuilder-Pro looks for and uses to open the gallery).
Incidentally, if you have changed the structure of your gallery since saving it (and use a configUrl or baseUrl to rename or move the configuration file), then JuiceboxBuilder-Pro will not be able to open the gallery.
However, as your gallery has a regular structure and your gallery's configuration file has not been renamed, you should be able to open your gallery as follows:
Instructions to open an existing gallery in JuiceboxBuilder (to edit it):
(1) Click the 'Open Gallery...' button on the 'Start' tab (or select 'Gallery -> Open...' from the drop-down menu at the top of the application).
(2) In the pop-up 'Select Gallery Folder...' dialog window:
Mac - Navigate towards and then double-click the gallery folder.
Windows - Navigate towards and then select (with a single left-click) the gallery folder (not a file within the gallery folder) and click the 'Select Folder' button.