Cover Your Tracks

Disable JavaScript and you're largely fixed. Amazingly enough there is a large enough contingent doing that such that you are far from unique (and it helps most all of the fingerprinting requires JavaScript)

I suspect there is something off with the browser fingerprinting logic which assigns high relevance to 'unique' characteristics like screen size while the reason for their 'uniqueness' is that the data is randomised on every request. Instead of assigning 20 bits to that single device with that odd screen size of 666x2045 (a different number on every visit) add a few bits to the variable 'randomises_screen_size' and ignore the screen size.