I believe the only feasible way without bending over backwards is to use the Tor Browser. But privacy and security always come at a price.
But it’s academic for me anyway, I have Accept-Language en-US,en;q=0.7,de-DE;q=0.3 which is close enough to unique that nothing else really matters.
TBB actually adds a border at the bottom of the browser so the reported size isn't the actual size. If you change the size of your browser window to the tor-reported size then it should work.
Unless I'm misunderstanding and you mean something to do with the scrollbar?