Does the job, could be better

As far as I can tell, it is necessary to set custom taxonomies to 'hierarchical' => true, in order for this to work on the bulk edit screen. No problem in my case but I can see that being a hurdle for less experienced users.

It also doesn’t appear to use the taxonomy labels, so the prompt text is always “Remove from category“, regardless of your taxonomy name.

Still, it did the trick and avoided the stupid delete-and-rename trick we normally would have to have used.