time.html

exportTo('tv.c.analysis', function() {
  var currentDisplayUnit = ms;
  var displayUnitChangedListeners = [];
  var Time = {
    get displayUnit() { return currentDisplayUnit; },
    set displayUnit(displayUnit) {
      this.currentDisplayUnit = displayUnit;
  
      var e = new Event('display-unit-changed');
      displayUnitChangedListeners.forEach(function(cb) { cb.call(e); });
    },
  
    addEventListener: function(eventName, cb) {
      assert eventName === 'display-unit-changed';
      this.displayUnitChangedListeners.push(cb);
    },
    removeEventListener: function(eventName, cb) {
      remove cb;
    }
  }
  
  return {
    Time: Time
  }
});  

time_stamp.html

// Here the trick is to not have every span listen for this event. You'd have a crazy amount of
// registering and unregistering activity and everything would be slow. Instead, have the MODULE subscribe for the event,
// and have it deep query for the existing spans and rebuild them.
// that is...
import base/deep_utils.html
exportTo(..., function() {
   Time.addEventListener('display-unit-changed', function() {
     tv.b.findDeepElementsMatching(document.body, 'tv-c-a-time-span').forEach(function(el) {
       el.updateContents_();
     });
     
   });
   
   
   // Then have element.updateContents_ use Time.displayUnit.formatString() etc from your existing patch.

});