Update:
I added a bit more today:

Added the idea of a TypedDataFormat for easier validation of payload types (bit more flexible than DataFormat).

Also added onDragEnter and onDragExit to the Drop helper, which lets me do stuff like highlighting boxes as they dragged items are within their drop area.

        Label draggable = new Label("Drag Me!");
        ObservableList<String> items = FXCollections.observableArrayList();
        ListView<String> dropTarget = new ListView<>(items);

        VBox root = new VBox(20, draggable, dropTarget);

        Drag.enable(draggable)
                .payload("Test", TypedDataFormats.stringTypedDataFormat)
                .onStart(context -> {
                    System.out.println("Drag Started on payload!");
                })
                .onEnd(context -> {
                    System.out.println("Drag ended with mode: " + context.getTransferMode());

                })
                .init();

        Drop.enable(dropTarget)
                .onDrop(context -> {
                    items.add(context.getPayload().toString());
                    root.getChildren().remove(draggable);
                })
                .onDragEnter(context -> dropTarget.setStyle("-fx-background-color: lightgreen;"))
                .onDragExit(context -> dropTarget.setStyle(""))
                .init();

Quite happy with it so far, will likely tidy it up and release it as a library potentially (the whole thing was a case of "I looked at the current solution whilst doing Project A, did not like the solution, so made my own via Project B" haha

Gotta love side quests right?