After some debugging: social_core.backends.google_openidconnect.GoogleOpenIdConnect works as-is, no change to the code is needed.
The issue I initially was running into is the same as mentioned in another recent post: when configuring the 3rd party provider, the "slug" must match the "backend_name". The latter is the one being passed into the process from the login form, and the former is the key in the table. The way the custom edx django-config model works, if the record is not found in the database, it returns a "new" object, which then errors out in the third_party_auth/strategy.py with the message "Can't fetch setting of a disabled backend/provider". After shaking off the initial confusion that there was something related to the social class mismatch and making the slug=backend_name - the Google OpenId Connect authentication worked. The setup is the same as for the Google OAuth2.