I've often thought about writing a trello-like whose backend was simply markdown or org-mode files that was versioned in a real version control system. There is nothing in the Trello UI that really precludes it (and in fact, there was at one point a program that allowed you to talk to the trello API and grab/push org-mode oriented data from Emacs -- I never found it worked particularly well, though).
I use org-mode files every day and it's a limitation I feel more and more.
Each board is a directory. Each column in a board is a file. Each task is a line in the file. Open up the directory in the text editor of your choice. Move tasks with your normal cut & paste commands that you use for everything else. Keep the whole thing in version control.
As a casual org-mode user, I fail to see how org-mode is really relevant for a team-centric tool.
https://trello.com/b/TTAVI7Ny/ue4-roadmap
This is not a good fit for org-mode, despite what any number of org-mode zealots say.
Some, including me, swear by it as the ultimate personal organizer, note taking, mind dumping application