Hi Samuel
I don't know much about Event Budgets (I don't think anyone does), but I can almost guarantee you that they are not the solution you are looking for.
However, there is a solution, and it has to do with JobCost. PO can flag an entry that would cause the amount to exceed the Job Estimate in JobCost.
So to get where you want to be (assuming you are not using JobCost for any other purpose), you would create one new job each fiscal year, and give it Phases/Categories that correspond to the GL Accounts/Departments, with the budget amount entered as the estimate. You would then code the PO detail lines to the correct Job (fiscal year), Phase (account), and Category (department).
I hope this makes sense. It's a bit of a workaround, but it does work.
Steve