So which content are you supposed to show to googlebot?

The same content that you would show to other users.

Googlebot's referrer is google.com, so it is able to bypass the paywall, just like anyone else clicking off google.com

Right. So is the correct "fix" for this situation perhaps for googlebot to stop sending this referer?

Google wants to see what the site will look like to someone who clicks to it from google, because that's what their users will be doing.