I've done that crossing. Used 2 BD ovals, clipped to the top cable. Pretty much any larger gate biner will work, and use your cordelette for the tether so you don't have to bring any special gear. Heard of someone who once brought a bike U lock over the whole traverse just for the cable (!)
I walked the middle cable. I think walking is the way to go, a friend tyroleanned the lower cable and found it hard work pulling his carcass and gear up the last half. If you walk, you just have to push giant balls and cones out of the way, kind of like being on Knockout. Nice to have 2 biners on separate tethers so you can pass the balls and cones while staying clipped in. Make sure your tether isn't too long either. Trying to prussic that if you fell off would be a tiring exercise in frustration. That leather glove trick is cool, have to remember that one...