If Google won't repair a manufacturing defect, consider a chargeback (assuming you bought it from Google).
Services like American Express have purchase protection, but the limits I believe won't be enough to cover the Pixel. If you were sold a lemon and Google won't hash it out, go ahead and let the card company fight that battle for you.
If enough people start doing this, you can bet Google will double down on customer service as proper cost avoidance.