I ran the numbers, and Louis XVI can postpone calling the General Estates by only one year if he doesn't participate in the American Revolution. Lots of butterflies possible with a one year delay, but it wasn't enough to significantly alter the system by itself.
The nobility don't pay tax in the ancien regime. Since the crown also never gives them real responsibility, reserving any post that matters for a commoner dependent on the crown, the not-paying-taxes is nearly their only privelege or responsibility, and they guard it psychotically in time of peace and pretty jealously in time of war. A business majority owned by a noble or nobles doesn't pay tax (which is why every major firm needed a noble senior partner).
The crown also disburses most of its revenue back to the nobility in the form of made-up posts and jobs and honors. The French military, for all its might, and the palaces like Versailles, actually don't amount to much in terms of total expense.
Even a modest tax on property that applied to nobles, or even making corporations with noble major shareholders pay tax, would have solved the problem. Cutting back on expenditures would have worked, but the idea is ridiculous; the whole purpose of the taille and some would say the entire purpose of the civil administration is to move wealth from commoners to nobles, who then spend it on personal luxuries and extravagances.
The heart of the problem is that, while annoying, no one with power really regarded this as a crisis-level problem. Commoners pay taxes to nobles, with the king and his intendants as the middlemen taking their cut. That's what France WAS in many eyes.
Not that I doubt you, but I'd like to see those numbers.