Interesting, since it makes me wonder if it could actually be usable if you stripped out Qt and flattened things "down" to a simpler widget set and rendering engine, but completely unusable on all my machines.
Can you elaborate?
Incrementally then using more of html canvas to speed things up might be next.
Most of the work is going to be having the GUI (toolbar/notebook bar, menues, sidebar, dialogs) browser-native of course.