I was comparing my newest run with the new run from Wailmernoir (both are up on Youtube) to see what we did differently, and I thought this might be fun to share. Sorry about the messy audio, these are recorded from our twitch streams, so we're both talking a bit.
I think you have to hit play on each one, then it will pause and wait for you to hit the play button at the bottom, and it should be pretty well synchronized.
https://viewsync.net/watch?v=ojKOi98MK0Q&t=4.34&v=oPDl69UJyrg&t=1.79&mode=solo
When you're trying to skip the dialogue scenes, don't just mash the jump button. That causes the images to slowly fade out. Instead, hit Escape (if you're playing on keyboard) or the back/options/select button (if you're playing on a gamepad.) That skips the dialogue entirely.
It's important not to hit it before the screen fades out to transition between worlds, though. If you do that, you'll actually be losing time, as it will pause the game to ask if you want to quit.