Joe, it would be a great help if you could put somes example on your website of how the plugin can be used. I've added the ability to upload Japanese subtitles using the functions.php code snippet you provided, and I uploaded subtitles in English and Japanese to be used with a YouTube video. Here's a screenshot of the configuration:
Here's a screenshot of the video imbedded in the post. There isn't an icon on the right side of the bar across the bottom of the video to choose to display captions.
However, if I go back to the admin page for editing the video configuration and add a URL for "Captions (SRT/DFXP)" then I can select captions.
I simply added a link to the same .srt file for Japanese subtitles. I don't understand what the difference is between "captions" here and the "subtitles" settings below.
Now I can select Japanese or English captions:
...but why does the selector for English subtitles show up twice?
I'm going off on a slight tangent next about the JPG overlay.
There's a div that uses an inline style tag to overlay an ugly lowres jpg provided by YouTube. It's what's returned when the URL for 0.jpg is 404. What's the best way to get rid of it?
<div class="mejs-poster mejs-layer" style="width: 100%; height: 100%; background-image: url(http://img.youtube.com/vi/https://www.youtube.com/watch?v=d0yGdNEWdn0/0.jpg);"><img width="100%" height="100%" src="http://img.youtube.com/vi/https://www.youtube.com/watch?v=d0yGdNEWdn0/0.jpg"></div>
This is what it looks like: