Thanks for this! I can see that you and I are somewhat on the same page in terms of mindset, though you're far ahead of me when it comes to both dev experience and math.
I looked a while ago and The Udacity nanodegree looks interesting but kind of a subset of the materials I'd already lined up. I also think part of the challenge is tailoring a curriculum to one's existing strengths, so in my case I'm spending less time on general programming / data munging, more on stats fundamentals and ML algorithms, and find that most all in one MOOCs have some material that is less worthwhile for me. Also: some of the projects they feature, like the kaggle competition https://www.kaggle.com/c/titanic can be undertaken independent of udacity.
I really think Python Machine Learning + https://www.kaggle.com/c/titanic + kaggle.com/c/forest-cover-type-prediction is a great place to start on the practical ML side.
http://karlrosaen.com/ml/