What I want to know is how to dynamically update the web browser from the Arduino board WITHOUT having to do the "META refresh" thing.
I don't think you can. The browser is a client. It makes a GET request. The Arduino as server responds to that request.
The returned page can contain data that causes the browser to make another GET request on a regular basis.
But, the server has no way to push more data to disconnected clients. Or even any way to keep track of who those clients were.