Base85 would probably be a better choice for storing binary as text, since it has a ratio of 5:4 instead of 4:3.
On the topic of "unusual and free large file hosting", YouTube would probably be the largest, although you'd need to find a resilient way of encoding the data since their re-encoding processes are lossy.
I like the "Linux ISO" and "1337 Docs" references ;-)
Here is an implementation of arbitrary data storage using YouTube videos: https://github.com/dzhang314/YouTubeDrive