I found a solution for shuffling videos between multiple YouTube playlists, in case anyone is in a rare situation where they need to do this. For some reason, YouTube caps the video count at 200 when you embed a playlist on another site, though the playlist may contain way more that 200. Embedding playlists also disables the shuffler.
I like to listen to some of my playlists at work, but streaming directly on YouTube is rather slow; embedding the playlists on a plnkr.co page is my workaround…but that brings the no-shuffle, 200-video-limit into the mix (har har). But with this randomizer, you can shuffle videos between any playlists, even from different users. There’s probably a way to do this programmatically using YouTube’s APIs, but I didn’t have the inclination to spend the time on it.
Here’s the permalink for my three playlists. It’s also neat that the page title changes with each video, so if I hear a song I’m not familiar with, I just have to hover over the browser tab in Chrome to see the title.