Settings

Call out the time every … minutes
One pip each call, three on the hour.
While the stopwatch runs and this page is in front.
Plays an inaudible tone so Chrome keeps the page awake. Adds a media notification with pause and play, and pauses other music while the stopwatch runs.

If calls still stop with the screen off, set Chrome’s battery use to Unrestricted: Settings › Apps › Chrome › Battery.