Looks like you are creating the labels as geometry set in the feeder. You could modify the part being created to have the geometry set. You could use, for example, a Statistics Display component to display info and attach it to the template part. When a part is created its child components are also created with it, hence the part and statistics display. So if you want to update the display in API, just find the child component of the part, and then edit the TypeMe property of the display.
But there are different ways to do what you want. In your code, the geometry is not in the part, which is why it does not move with the part.