Why does the fact that GTK "looks non-native on Windows" disqualify it? If it's pretty enough for Linux, isn't also good enough for Windows? (Also my personal opinion is that it doesn't look too bad.)
Non-native breaks consistency, rendering 'pretty' fairly meaningless.
Not personal but I can't resist: "A foolish consistency is the hobgoblin of little minds." (Emerson)
(Case in point: the very website's scrolling. Works great on desktop Firefox, not obviously distinguishable from any other website. On iOS... a sad joke, made at the user's expense.)
Spotify
Microsoft Office
NetFlix
Chrome
FireFox
...the list goes on. There is no such thing as a standard UI or behaviour at this point.
Any one that owns a mobile device already has to be used to a mixture of UIs every time they switch between devices or specific applications.