In a nutshell, Meta Slider is missing a UI for managing trashed sliders.
To elaborate, I had noticed that my WP database contained far more ml-slider_settings and ml-slider_type entries than there were sliders on the Meta Slider page. I then recalled that some time ago, I had deleted a number of sliders which I didn’t need anymore, and so I presumed that those sliders were still being stored in the database.
A bit flustered by this, I proceeded to examine the main plugin file for Meta Slider (ml-slider.php) and found that when a slider is deleted, it is moved to the trash. However, I always thought that deleted sliders were deleted permanently—there was no indication in the interface that they were being moved to a separate trash.
Oh, and by the way: I finally was able to delete my trashed sliders via this URL: