I think your solution is really interesting, although I wonder if all the characters would be able to fit. It might work if there's a bit of a 3D effect, where part of the loop appears in front, and part of the loop appears behind and faded a little bit so it looks like it's a bit behind the screen. It would also probably allow for some loops that could be shown above to detail the history of the characters you entered.
That's awesome that our algorithms ended up being really quick! I guess we underestimate the power of machines, haha.