The funniest part is that in the followup post, he writes that the IRS looked at this, say "Shit, you're right," and spelled out the iterative method. Which you iterate until convergence, though you can stop after two rounds if you're lazy and want to leave money on the table.
That's the funniest part: the IRS agreed that that was the correct method, based on how the law is written. "This is stupid. But it's what we gotta do. Just cycle it a bunch."