Make QWebSocket::QWebSocket(QTcpSocket...) accessible

I would like to develop a built-in HTTP server for my Qt application, but I also need WebSockets functionality. Qt's WebSocketServer cannot be integrated into another HTTP server on API level, only by proxying (which would be stupid).

So I wanted to do the websocket handshake in my HTTP server and then hand over the connection to QWebSocket. Sadly, the needed constructor that takes a QTcpSocket is private.

It looks as if someone made deliberately made Qt WebSockets as difficult to extend as possible. It only supports a single use case: run a WebSocket-only server or make outgoing connections.