How to copy objects from one layout to another with rhinocommon?

This should work nicely if you know the old and the new Viewports.

var oldView; // Viewport to Copy from
var newView; // Viewport to Copy to

// Get old objects
var doc = Rhino.RhinoDoc.ActiveDoc;
var enumerSettings = new ObjectEnumeratorSettings()
{
  ViewportFilter = oldView;
};
RhinoObject[] oldItems = doc.Objects.Find(enumerSettings);

// Add new objects
var attribs = new ObjectAttributes()
{
  Space = ActiveSpace.PageSpace,
  ViewportId = newView.Id
};
foreach(RhinoObject obj in oldItems)
{
  var geom = obj.Geometry.Duplicate();
  doc.Objects.Add(geom, attribs);
}