Amusingly so far my privacy has been best protected by Mobile Safari on a popular iPhone model on the latest OS version:

"Within our dataset of several million visitors, only one in 857,908 browsers have the same fingerprint as yours."

As it doesn't allow for plugins, my fingerprint should (cookies aside) match that of any other <popular device> user.

So maybe the solution here is coming up with a 'secure browse' profile that every browser reports the same fake fingerprint.

Security in numbers.