I simplified the story a bit for brevity. I actually tried a bunch of different font styles, including a 47 page fax using a pretty large size Courier (with only 72 characters per line). The screenshots from the blog post were after the point I decided OCR wasn't working, so I was using a heavily reduced font size to optimize the transfer time. Hence the characters looked like barely-legible blobs.
The Fax-to-Binary converter isn't doing anything particularly complicated with the image, just breaking it up into an accurately-aligned grid and hashing the pixel data of each tile.
Replacing the characters in the document hadn't occurred to me at the time! It's a good idea, but for my programmer brain, writing this software was the easier (and more fun) solution :)