Starting playback will in 9/10 cases run the visuals too early, with the sound lagging behind.

Start when everything is ready, not when audio is ready

It's possible this is a race issue and HTMLMediaElement.play() can be called along with the first executing Monkeydo task to make them play together.

Time drift

It is however also quite possible this is related to setTimeout() drift. Which can be observed even with the audio and visuals in sync by simply placing the browser in the background or even triggering some work on the main thread.

If this happens to be the case, one solution could be to implement a current time "sync pulse" which will be emitted from a Monkeydo task (with some interval) containing the expected media currentTime for an adjacent task.
HTMLMediaElement.currentTime could be aligned with this pulse, but it might cause a lot of audio glitches.

Pop-up blockers prevent window.open() to open windows

Most browsers ship with pop-up blockers built-in and will usually only allow a single window to open (or none at all).
Chrome will send out a permission request to the user asking for the "open multiple windows" permission.

The Multi-Screen Placement API looks like possible candidate to fix this issue if its permission query also applies to opening windows, and not just placing them.

navigator.permissions.query({ name: 'window-placement' });

Since this demo relies on browser windows, being able to open them is quite crucial.