I think that what threw Madison's calculations astray was the advent of party politics - such things as political parties within the United States were yet to form and Washington, for one, hated the very idea. If one's primary political identification is with the branch of government in which one works, there is a natural tendency toward defending one's turf. Throw party identification in there and it's another story. A Senator would, ceteris paribus, have no reason to wish to stretch a little political power just because a President wanted it, but a Whig Senator might want to do so for a Whig President, or a Democrat for a Democrat. Someday soon even the Republicans may master party politics.
You can see how that upsets the balance. In come ways it may be a good thing, but what it does to the separation of powers isn't one of them. IMHO, of course.
We'll see in the next paper how Madison does foresee a dynamic within the Virginia constitution that party politics did end up subsuming, in the form of how few people it might take to prevent the remediation of an untoward assumption of power in that government. (Cue Announcer Voice: "Tune in Thursday for another thrilling chapter...") :-)
Oh, well, typos are an excuse for another BTT.
Washington did indeed hate the very idea of factions in government. Madison however was a very strong advocate for them thinking that they would serve as yet another check on runaway government so I doubt very much that his thinking was overtaken by them having arisen.
....and their pet mutations that hunt for power and income.
Our federal government has a limited design. Not much money to be made there....unless it is "living and breathing."