I have previously mentioned webviewextra to you.
The only other thing I can think of, and have not tried it, is to inject some javascript into the web page with the link or links you want to download. The javascript should contain a listener that can capture the full urls when clicked, return these via the webviewstring, and then the urls could be passed to the web component for download.
Something like:
document.body.addEventListener("click", function(event) {
event.preventDefault();
window.AppInventor.setWebViewString(event.target.href);
});