move same layer (on timeline) in multiple compositons at the same time

You can use this script:

Select some layers in your active composition as reference layers.

Then run the script. It will loop through all your compositions and move layers that have the same name and label color  as your reference layers.

(in case it doesn't work as expected, you can undo the operation)

Move Identical Layers.jsx

(function(thisObj) {
  buildUI(thisObj);

  function buildUI(thisObj) {
    var palette = (thisObj instanceof Panel) ? thisObj : new Window("palette", "Move Identical Layers", undefined, { resizeable: true });
    palette.margins = 5;
    palette.spacing = 5;

    var moveLayers = palette.add("button");
    moveLayers.text = 'Move Layers';
    moveLayers.preferredSize.width = 120;

    var checkbox1 = palette.add("checkbox", undefined, undefined, {
      name: "checkbox1"});
    checkbox1.text = "Skip Locked Layers";
    checkbox1.value = 1;

    if (palette instanceof Window) {
      palette.center();
      palette.show();
    } else {
      palette.layout.layout(true);
      palette.layout.resize();
    }

    moveLayers.onClick = function() {
      var proj = app.project;
      var thisComp = proj.activeItem;
      var refLayers = thisComp.selectedLayers;
      if (!refLayers.length) {
        alert('Please, select at least 1 layer');
        return false
      }
      app.beginUndoGroup("undo");
      for (var i = 1; i <= proj.numItems; i++) {
        if (proj.item(i) instanceof CompItem && proj.item(i) !== thisComp) {
          for (var j = 0; j < refLayers.length; j++) {
            for (var k = 1; k <= proj.item(i).numLayers; k++) {
              if (proj.item(i).layer(k).name == refLayers[j].name && proj.item(i).layer(k).label == refLayers[j].label) {
                var locked = proj.item(i).layer(k).locked;
                if (locked && checkbox1.value) {
                  continue
                } else if (locked && !checkbox1.value) {
                  proj.item(i).layer(k).locked = false
                }
                proj.item(i).layer(k).startTime = refLayers[j].startTime;
                proj.item(i).layer(k).inPoint = refLayers[j].inPoint;
                proj.item(i).layer(k).outPoint = refLayers[j].outPoint;
                proj.item(i).layer(k).locked = locked
              }
            }
          }
        }
      }
      app.endUndoGroup();
    }
  }
})(this);