Where you able to get the scriptlistener log to output using the layerSet name in the to reference or did you edit the log file? I have only been able get it to output index. And it doesn't seem to work by name. I would do something like this.
var sourceLayerSet = app.activeDocument.layers.getByName('Star');
var destinationLayerSet = app.activeDocument.layers.getByName('Star.psd');
moveLayerSet( sourceLayerSet, destinationLayerSet );
function moveLayerSet( fromLayer, toLayer ){// layerSet objects
var desc = new ActionDescriptor();
var sourceRef = new ActionReference();
sourceRef.putName( charIDToTypeID( "Lyr " ), fromLayer.name );
desc.putReference( charIDToTypeID( "null" ), sourceRef );
var indexRef = new ActionReference();
indexRef.putName( charIDToTypeID("Lyr "), toLayer.name );
var layerIndex = executeActionGet(indexRef).getInteger(stringIDToTypeID('itemIndex'));
var destinationRef = new ActionReference();
destinationRef.putIndex( charIDToTypeID( "Lyr " ), layerIndex-1 );
desc.putReference( charIDToTypeID( "T " ), destinationRef );
desc.putBoolean( charIDToTypeID( "Adjs" ), false );
desc.putInteger( charIDToTypeID( "Vrsn" ), 5 );
executeAction( charIDToTypeID( "move" ), desc, DialogModes.NO );
}