Edit: this has been worked into a set of scripts for downloading here.
One of the other weird ideas I had (which was more possible for me to implement at this stage) was to visualize the content of binary data in a way that showed its characteristics at a glance. Analyzing binary data appears to be one of the things you do a lot in DFIR work when you are faced with cryptanalysis tasks.
A couple of questions that came to mind when looking at a set of binary data were:
Which offsets had relatively constant binary values?
What are the range of binary values that can be observed from these offsets?