I looked at the boxes. Each pair was 13 Medium. Now, I was reasonably confident this wasn't going to work, but I figured I'd give it a try. The New Balance shoes were too tight. The other pair wouldn't even go on my feet. This wasn't a surprise.
Another clerk came back to see if anyone needed help, since a crowd was starting to gather. I popped up and told him that I needed a 13 Wide and the other fellow had brought out two pairs of 13 Medium shoes. He went back to the rear, then came out and announced that "They don't make walking shoes in 13 Wide." I loudly told him that was absurd and walked away.
When I got home, Gretchen directed me to Zappo's, where I found and ordered a pair of New Balance walking shoes in 13 Extra Wide. I'm wearing them now and they fit just fine.
The interesting thing, though, is that I have a tendency to wear away the outside of each heel in most shoes. But in these, I feel like I'm walking with my feet turned in toward my instep. Ok, that's different. We'll have to see how it works and how the shoes wear.