Well, after hours of downloading and having Twitter nearly crash my browser multiple times, I have collected together (almost) all of the 2016 birthday art.
Occasionally somebody will post something super late or I might find something on Twitter that I missed, if that happens I will add it to this folder so it might be worth waiting a few days before you download it.
Click "Download as ZIP" in the top right and enjoy!
https://mega.nz/#F!z84GQKxQ!KNTfXs7z6r7-e9D1MbXFig(I'll add this link to the "Useful links" pastebin in the OP, which also contains links to folders containing last year's birthday art, and a large collection of screenshots if you're interested.)
