The other ideas are more elegant than mine, but, what about mounting the chips on the same board as the LED's? I have done that in the past, that makes the wires all short. I also put the wires in bundles with tie wraps so there is not the wild look, been doing the bundles thing for years
Last project was I think 27 LED's times two wires in a marine chart, put the wires in bundles and it did not look all that bad, should be a link I think to my web site in my name - look for the ATON display if you want - back maybe 10 posts or so
good luck with your project