How to make StackSwitcher tabs closeable Gtk/Vala - gtk

Question

I am trying to make a Stack and StackSwitcher whose pages associated tabs can be added and deleted dynamically. To delete the associated widget in the stack and the tab in the StackSwitcher, I want to have a small delete button in the tab. I have found an example similar to this in the gtk3-widget-factory, screenshot shown below.
However, this uses a Notebook and I would like to be able to use the Stack/StackSwitcher setup instead of a Notebook (I don't like how the Notebook creates a background to its pages). I can't figure out how to change the widget that is displayed in the StackSwitcher for each page in the Stack. My intuition is that I should just be able to replace the Label in the StackSwitcher with a Box that has been packed with a Label and Button that has a callback that goes and removes the page and the tab. But I am not able to do this with how I am currently creating the pages of the Stack, which is by calling stack.add_titled(). The StackSwitcher that has been assigned to that stack just automatically picks up the labels with no way of editing them that I have found.
Is there a way to do this for a Stack and StackSwitcher? If not, I would also appreciate some advice for doing it with a Notebook as I have not even been able to recreate what I saw in the widget factory (above). This is the code that I have attempting to recreate it:
void main (string[] args) {
Gtk.init (ref args);
var window = new Window ();
window.title = "Example Program";
window.border_width = 10;
window.window_position = WindowPosition.CENTER;
window.set_default_size (350, 70);
window.destroy.connect (Gtk.main_quit);
Notebook note = new Notebook();
Box tabBox = new Box(Orientation.HORIZONTAL, 0);
Label tabLabel = new Label("Closable Tab");
Button closeButton = new Button.from_icon_name("window-close-symbolic", IconSize.BUTTON);
tabBox.pack_start(tabLabel, false, false, 0);
tabBox.pack_start(closeButton, false, false, 0);
Label displayLabel = new Label("this page should be closeable");
note.append_page(displayLabel, tabBox);
window.add(note);
window.show_all();
Gtk.main ();
}
which just creates an empty Notebook tab like this:
and I don't get any error messages about creating that tab failing so I don't know what to do. Any help is appreciated.