I was also looking for a way to combine a WSGI application with Streamlit. This thread clarified that I was making the wrong assumption that Streamlit was using a WSGI-compatible web server.
The Tornado web framework and HTTP server together offer a full-stack alternative to WSGI. While it is possible to use the Tornado HTTP server as a container for other WSGI frameworks (WSGIContainer), this combination has limitations and to take full advantage of Tornado you will need to use Tornado’s web framework and HTTP server together.