Thanks for posting this!! Was actually searching for this the other day here on HN and found a link to the https://github.com/mml-book/mml-book.github.io. haven't checked it out yet but the links in the OP look solid.
Like I commented above I haven't had a chance to go through the https://github.com/mml-book/mml-book.github.io book yet. But now that I have read your article in full I think diving headlong first with ML and then back filling the Math/Stat/Prob holes is the best approach to learn ML engineering. Like SICP authors mused about modern software development as being "programming by poking at it using APIs" instead of just lesrning to program just for the heck of it.