> It overrides alert() but doesn't - and can't - duplicate its blocking behavior.

If you really wanted to, I think you could set up an endpoint on your server to be long polled with synchronous XHR in a while loop, while you set up the popup in an iframe. When the popup is clicked, you send a notification to the server so the next synchronous request returns 200 and you dispose of the iframe.

On searching, I discover someone else has had this crazy idea already - http://stackoverflow.com/questions/16934667/what-methods-are...