Special blending mode (Overlay) for UIView with app background

I would like to blend a UIView with my app's background, using a special blend mode (in my case, the Overlay mode). However, the view to blend is contained in a complex hierarchy of views.

Blending a view with its direct siblings can be achieved using

view.layer.compositingFilter = "overlayBlendMode"

To recreate the problem, I made the following playground:

import UIKit
import PlaygroundSupport
class MyViewController : UIViewController {
  override func loadView() {
  let parentView = UIView()
  parentView.backgroundColor = .purple
  // Child view
  let childView = UIView(frame: CGRect(x: 50, y: 50, width: 200, height: 200))
  childView.layer.borderColor = UIColor.orange.cgColor
  childView.layer.borderWidth = 3
  parentView.addSubview(childView)
  // Child child view
  let childChildView = UIView(frame: CGRect(x: 50, y: 50, width: 100, height: 50))
  childChildView.backgroundColor = .white
  childChildView.layer.compositingFilter = "overlayBlendMode"
  childView.addSubview(childChildView)
  self.view = parentView
  }
}
// Present the view controller in the Live View window
PlaygroundPage.current.liveView = MyViewController()

Screenshots of what the result should look like are available here.

Note 1: the blended view is supposed to move, because it's inside a UIScrollView.

Note 2: my app background could be a gradient or an image, so I can't just change the color of the child view to make it the same as background.