Casey,
Your oauth2service.json file is incorrect. Any button/icon that says download with a servce account downloads a client_secrets.json, not an oauth2service.json.
I've only been able to get an oauth2service.json file at the moment of key creation.
The instructions explain how to get an oauth2service.json if you start from the beginning; if you didn't get the first one successfully, follow these steps.
Log in to the developers console.
When you sign in, you should be at the Projects screen; click your project name.
This should bring you to Home; click Enable APIs and get credentials like keys.
Click Credentials
At the end of the line that says "Service account keys"; click Manage service accounts
At the end of the line that has your project name; click the three dots and choose Create Key
That's your oauth2service.json after renaming.