Storefront Category slug-sort complications

In an effort to make a pull-down Category menu sort in the order I wanted it, I changed the Slugs for the Categories. It seems to have semi-duplicated them, and now I get them listed first alphabetically and then by Slug, so each has two listings in my drop-down.

When I go to Categories in Admin I get 138 Categories listed, but as soon as I sort, by Name or by Slug, this drops to 70 and the duplicates disappear. Anything I do to a Category happens to its duplicate as well, so I can’t just delete the duplicates. I did that once, and both disappeared so I had to completely rebuild the Category. The duplicate did not reappear, so I suppose this would be a solution, albeit a cumbersome one.

So how can I get rid of the duplicates and make the drop-down sort by Slug?