Theme mod to select multiple videos

My client wants me to insert a video slider into the Entry Header of their front page. Why? Not sure, but that’s where they want it.

I know how to use the customizer to select an image and store it as a URL in a theme mod option, but what I’d like to do is create a control that will do the same thing for *only* videos, and allow them to select multiple videos and return an array I can loop through to output them into the slider code in PHP.

I’m guessing I’ll be using the WP_Customize_Media_Control class and wp_get_attachment_url(), but I don’t know where to start with either setting it for just videos (if possible) or using it to select multiples.

If I can’t cleanly use the Customizer (e.g. handling deleted images), I might have to simply query uploaded media using a specified tag, which I’d like to avoid.