Did I turn them off somewhere?
I'm pretty sure I botched a setting because selecting to display claims to work, but then my posts still have just the bare zombie.

Account settings, settings, "use avatar borders" is set to Show.

Settings, Border Wardrobe:

In here, on the left, there's the bronze border, level borders shows that too, but the picture above "current level" shows a bare avatar with just the gem.

*points* but there, and in comments, I don't even have the reputation gem showing.

Feel I've got something messed up somewhere?

Go here: https://www.royalroad.com/account/options 
Under General, select "Show my Border to all users" and then save changes. 

Thank you, I knew I had to be missing something.

can't tell you how many times I missed "show my border to all users"