OK, so a Plan B can be to use saved table to table imports. They are very fast and powerful.
So that technique involves making a single Admin record to hold some Formula URL Buttons which are each steps in your central app.
So for example
Button 1 Purge all tables in your Central App
Button 2 Import all Projects from Department 1's app into Projects
Button 3 Import all Tasks from Department 1's app into the central app.
Then similar pair of buttons to import the projects and tasks from each of the department app.
The planning challenge here (which is not insurmountable) is that the Key field of the Projects table is Likely to not be unique across applications, unless you are very lucky in your planning.
So each month when its time to consolidate, someone (probably you) just pushes say 10 button and in literally a minute the app is purged and refreshed.
What I have done in similar multi step reloads is to have each respective URL formula button also update the current date and time onto the single Admin record and for good measure I make a nice green checkmark if the button has been successfully pushed that month.
So you just push the buttons and get a checkbox and push the next button.
In my app I even have the very last button update a field which triggers an email notification which emails the manager that the app has been reloaded.
I can show you a demo of that if you like and what a saved table to table import looks like. Contact me off line via the gmail address on my website. QuickBaseCoach.com
The point is that ongoing synching is technically difficult, but pushing even 10 buttons mindlessly at month end is easy.