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.
Yes, perhaps I could have been more clear here. As I mentioned in the post, while technology is certainly not new, it's more accessible, such that creators have access to it as a new medium.