Multi-JFrame/JFXPanel app leaks JFXPanels

The following application dumps OutOfMemoryError after about 40 seconds:

public class LeakTest extends Application {
    
    private JFrame frame;

    public static void main(String[] args) {
        launch(args);
    }
    
    @Override
    public void start(Stage primaryStage) {
        primaryStage.setScene(new Scene(new Group(), 500, 500));
        primaryStage.show();
        
        Timeline timeline = new Timeline();
        timeline.setCycleCount(Timeline.INDEFINITE);
        EventHandler<ActionEvent> handler = new EventHandler<ActionEvent>() {
            @Override
            public void handle(ActionEvent e) {
                SwingUtilities.invokeLater(new Runnable() {
                    @Override
                    public void run() {
                        recreateFrame();
                    }
                });
            }
        };
        timeline.getKeyFrames().add(
                new KeyFrame(Duration.millis(1000), handler));
        timeline.play();
    }

    private void recreateFrame() {
        if (frame != null) {
            frame.dispose();
        }

        final JFXPanel jfxPanel = new JFXPanel();
        
        frame = new JFrame();
        frame.setSize(500, 500);
        frame.getContentPane().setLayout(new BorderLayout());
        frame.getContentPane().add(BorderLayout.CENTER, jfxPanel);
        frame.setLocationRelativeTo(null);
        frame.setVisible(true);
        
        Platform.runLater(new Runnable() {
            @Override
            public void run() {
                GridPane gridPane = new GridPane();
                for (int i = 0; i < 10; i++) {
                    for (int j = 0; j < 10; j++) {
                        gridPane.add(new TextArea("test"), i, j);
                    }
                }
                Scene scene = new Scene(gridPane);
                jfxPanel.setScene(scene);
            }
        });
    }
}

Profiling suggests that TextAreas, JFXPanel, and Scenes created by the application are never garbage collected and are held by the java.awt.dnd.DragSource.dflt static field via SwingDnd and a chain of DnDEventMulticaster objects.

The problem was originally reported against WebView running inside JFXPanel but appears to not be WebView-specific.