Biohackers Netflix - DNA to binary and video
I was quite curious when I saw that as well. I've spent more time than I'd care to admit trying the sort of things you have. I've gotten it decoded now, but I can't really claim any sort of victory, as the problem was pre-solved.
After struggling through some of the same experiments you did, I decided to take a closer look at their explainer video here: https://youtu.be/DMYgjOHgHxc
First I tried to decipher the blackboard sketch around 1:30, but it was quite vague. A closer investigation into the speaker, however, yielded some luck. Googling Dr. Reinhard Heckel brought me to his website here: http://www.reinhardheckel.com/ which shows his most recent publication – a paper on encoding digital data in DNA.
The encoding is relatively complex (something nearly impossible to stumble upon accidentally, I'd reckon) but fascinating. The fragments are indexed and have two, layered error-correcting codes. Perhaps making our job harder (but serving the practical purpose of minimizing homopolymers and unwanted annealing) is the fact that the data is XORed with a pseudo-random noise that shuffles the data. The paper obviously has all of the details.
From my skim, however, I stumbled across this Github repo linked in the paper: https://github.com/reinhardh/dna_rs_coding
As it happens, the README was just updated in this last week, describing how to decode the episode from the file provided. If you have Docker, you just need to copy-paste some commands.
The product is indeed the full and final episode – coming in at a dainty 63.1MB. How did they get 40 minutes of video that compressed? Well, in short, 720x360 at 24 fps. It looks a little awful and is in German only, but is certainly a cool little easter egg. If nothing else, I have a cool paper to read.