Integrating Video.js with Google Analytics
I think I answered this after I posted. I was trying to use the ID on the &lt;video&gt; itself, but I instead tried using the ID of the div that contained the video, and that worked without issue. I still need to figure out how to update the code dynamically on a per-page basis so that the correct video is tracked, but it's at least working now.

EDIT: I was able to modify the "inline" code file from above to automatically pick up any videos on a page that the script is loaded on.

(function ($) {
    $('.video-js').each(function() {
        videojs(this.id, {}, function() {
          this.ga(); // "load the plugin, by defaults tracks everything!!"
        });
    })
})(jQuery);