Question: The two things I'd like to do in particular are:

* slice up an individual video into many smaller videos
* Draw basic shapes on top of the video

I would prefer to use python because I already know it and it is well-suited for the rest of the work that is happening around this video.

Answer: 
Try [Media Lovin' Toolkit](http://www.mltframework.org/), which has Python bindings.
Maybe OpenCV could help you.

The main project page : <http://opencv.org/>
And the bindings for Python : <https://code.google.com/p/pyopencv/>

Cheers,

K.