Return the browser-oriented part of the response sooner.

Browser clients don't actually care about our HTML snapshot, so we can
return the part they do care about as soon as its' ready and then follow
up with the rest of the body later once we have it. In browsers this
will be ignored because we will have replaced the document with the
template by this point.
Hide the HTML snapshot from JS-aware browsers using a fake script.

Previously we were trying to asynchronously overwrite the document with
a new document, but that caused glitchy behavior in various browsers,
including crashing Google Chrome altogether.

This approach seems to make browsers happier. (Tested in Google Chrome
and Firefox on desktop so far.)