You'll need to find another provider which doesn't care that much about preventing phishing attacks. Google accounts are a big target so it makes sense you move away from the masses.
In practice it just means faking the user-agent and other fingerprinting more enthusiastically. I'm not sure how google can win that without resorting to the same anti-cheat measures as games companies.
You'll try, but the first time you won't know what fingerprinting tests they are going to do. After a few iterations you'll succeed, but it will be obvious to Google that the account you've just been testing it on belongs to someone trying to break their auth restrictions...