Custom Taxonomy

I need to create a custom taxonomy.
I need to have the (mostly normal) taxonomy select box appear when editing a post but I need the taxonomy to be hidden in all other ways.
So, someone can select a term in the taxonomy, like they would select a category but, there is no admin UI, they cannot add or remove terms.
I need to use the standard select box because this will interact with Advanced Custom Fields to allow the display of custom field groups based on the term selected. The actual terms that are added will be controlled by the plugin.

I’ve found plenty of things about custom taxonomies and moving the box, but nothing that will do what I need done. show_ui set to false hides everything and then I need to build it myself, building my own select box means that it will not interact with other standard things like the standard box will unless I also custom build all that interaction.

It seems like this should be possible through the register_taxonomy() function. However, there seems to be a very narrow view of the way taxonomies should work.

Can anyone help me do this without needing to reinvent the wheel?