Hi. I just wanted to revive this topic a bit by sharing a website that can convert playlists across platforms and might make the issue with exporting playlists a bit easier to tackle, or at least give you an idea of where to start.
Aside from that, I’ve used a few tools that require you to log into your account and authorize the tool, then it can manipulate playlists and things for you.
Without authorizing something, youtube API limits unnamed playlists to 50 items, and I’m not sure about other platforms.
Example: Parse Youtube Links and Create Playlist - Chrome Web Store
How the 50 limit playlist works: How to create a YouTube playlist from a list of links? - Web Applications Stack Exchange
You could have something parse through the links in the watch2gether playlist and generate playlists for the different platforms in increments based on the respective API limits.
I would love to see this implemented, and best of luck in doing so if it is still on your to-do list!