the only way to do this is to replace document.write with your own function which will append elements to the bottom of your page. It is pretty straight forward with jQuery:
document.write = function(htmlToWrite) {
$(htmlToWrite).appendTo('body');
}
If you have html coming to document.write in chunks like the question example you'll need to buffer the htmlToWrite segments. Maybe something like this:
document.write = (function() {
var buffer = "";
var timer;
return function(htmlPieceToWrite) {
buffer += htmlPieceToWrite;
clearTimeout(timer);
timer = setTimeout(function() {
$(buffer).appendTo('body');
buffer = "";
}, 0)
}
})()