I was hoping to be able to crib from the existing Octoprint UI, but I can't find any .YAML files that generate the controls. I even did a search through all the files in the .octoprint folder tree for some of the button text, but found nothing.
Any idea where this control generation code resides?
There is no such yaml, they are defined in the source.
That's where it starts, though it is a lot more complicated than your custom controls. At the bottom of the file there is a template for the custom controls, if you can make sense of it, might give some hints as to what will make what etc.