Two thoughts:
I always imagined something like this should use the <object src="app.jar" /> tag. If you consider that someone could build a browser again with java in it, (like I have) then it would be good to design a polyfill such that, it allows for a native version to exist (and then doesn't run) Also using the same mimetype for jars, classes and source files seems non optimal.
It would be really good if gwt,doppio,teavm all agreed on a single api facade for targeting the browser API. I think that would really put some steam behind the underlying idea here.