I'm not totally sure what I'm looking for but here are some ideas the internet has:
https://stackoverflow.com/questions/30086861/youtube-js-api-play-by-random-time-point-on-button-click

https://stackoverflow.com/questions/44197831/randomize-slick-slides-except-the-first-slide

I went a little more conventional/familiar and used Slick Slider to handle the rotation bit.  ACF for the slides (repeater) which doubles as the Block component.  For ordering, I randomized a starting point based on the number of slides, and build the slider incrementally from that point (as opposed to always the start), and then start at the beginning to collect any remaining slides.  This keeps the order intact, and we don't have to figure out where to start the slider, as it's been pre-determined so the slider functionality is standard.  The only thing special here is that when a slide hits a video, we pause the slider and play the video.  When the video completes, we resume the slider.

It's currently using a 3 second gap slide duration, which works well when it's only videos.

I kind of stopped there as I didn't know what sort of size/styling they would need, and also how to handle non videos.  Perhaps I'd have to pause the slider for a set duration. 

https://icsc.diocesanweb.org/basic-page/

conference-slides.jpg 170 KB • Download

New Notes
- Will be using videos since they are exhibitors are sending over Powerpoint Slides (can be exported as videos since some have animation)

I've requested that they send us the slides in video format as soon as they get them for testing. 

Thanks, Ryan!

Went through the process of converting a slideshow to video with Shannon
Uploaded to site and tried here: https://icsc.diocesanweb.org/basic-page/

We might need to get one more video before making sure the randomization is working correctly

https://icsc.diocesanweb.org/basic-page/
I added a third video but it doesn't seem to be starting at different points and playing the videos. It shows a second of an image then goes to the next one. 
Since they're videos, we want to randomize the order of the slides (videos)  now?

Good catch.  There was a fundamental flaw with my initial code that caused that first slide behavior.

I've modified it so that the slider itself is set to NOT autoplay.  I already had the part watching for video ended to resume slider play, so I just changed that to "Next Slide".  The part that watches for new slide and playing the video still applies and works fine.

These adjustments fix the issues and eliminate the lag in between videos as well.  A hard refresh will do that trick and see the updated functionality.

My sample video slide wasn't playing when not logged in.  Strange.  I've removed that slide.

There are currently two slides and the order will always be same (not that you can tell from a sample size of 2).  The initial slide will be random, and then cycle through from there infinitely.

Given 5 slides, in order A B C D E, one will randomly be first, and fill in from there.  So one order with 5 possible starting slides.

ABCDE {repeat}
BCDEA {repeat}
CDEAB {repeat}
DEABC {repeat}
EABCD {repeat}

If instead they want completely random, we can do that too.  (120 combinations using ABCDE)

This should work for them, especially since they plan on having at least 10 videos. 

I just added 2 more videos (total of 4)

Added more videos.

For mobile, can we have the videos resize so they don't get cut off?

Resize done.

I think this item is good to go!