Certainly that would be preferable.
When I think about all the issues you are struggling with.... I go back to my history. I was the comptroller in the Province of New Brunswick for five years. I was deputy minister of finance and secretary to the board of management for one year. I've had to live through all these issues about preparing budgets, preparing estimates, and preparing financial statements.
Certainly the practice in New Brunswick with preparing the budget was that both the budget and the main estimates were prepared at the same time. If you looked at the expenses in the budget, you could then go to the main estimates book and see the same number for expenses in the main estimates book. You could add up all the departments and you could see how that number was arrived at. Everything was agreed to at the same time.
Of course, then it takes some time for the estimates to get through all the estimates process and get voted in the legislature. The Financial Administration Act in New Brunswick provides authority for the comptroller to continue paying expenses for any program that existed before the start of the fiscal year. They can continue making those payments for the first three months of the fiscal year, so it allows the business of government to continue.