Instead of learning how those Python modules work in a vacuum, you could pick a project that utilizes something from each of them. Pick a topic you're interested in and do a deep analysis of it using numpy, scipy, sklearn and pandas. Sprinkle a little matplotlib in there to plot the results.

For example you could scrape a bunch of data off of your favorite subreddit and do a network analysis of all the users. It'd touch on a lot of the packages you want to learn and you'd be learning them for a specific end result. You could even throw the data into Gource at the end for a cool visualization (not that it would be very instructive, but it's cool to watch).

Also it's only 3 months. Just my perspective but I think you'd get a lot more out of it by sticking to one language and learning it really well.