Been looking at wrenches on Amazon. Most of them look like mine. I added "thin-wall" to the search and it came up with this set:
https://www.amazon.com/HORUSDY-11-Piece-Wrench-Combination-Organizer/dp/B0C9W2C34M/
More cheap Chinese tools, but I figure for what they cost, if the set's 7/16" box end works on that one nut, I will consider it money well spent; otherwise, I'm out only fourteen bucks. To my eye, these 12-pt box ends do look perhaps a millimeter thinner than on the ones I have. They'll be here tomorrow and then we'll see.
Why, you may be asking, does LN use both metric and SAE? That's a good question. The oil-line fittings are metric, but the Solution Supplemental kit provided a 7/16" deep socket specifically for that one nut, which came in the bearing kit for the stud. Wish they had included a 7/16" box end that I could get on that nut.