Using new Oauth2 endpoint to get Access Token--400 error

So far in our Constant Contact integration, we have been successful with the older 'idfed' Oauth2 endpoint for retrieving access tokens with a POST.   However, during the maintenance outage yesterday learned that we had to switch to use a new 'authz' endpoint by March 31st, very surprising to hear of this.

So far, in trying to adapt to using the new 'auth' endpoint, we get 400 errors in testing.

I have this POST:

https://authz.constantcontact.com/oauth2/default/v1/token?code=AUTHCODE&redirect_uri=URI&state=STATE_ENCODED_VALUE&nonce=NONCE_ENCODED_VALUE&grant_type=authorization_code

(the UPPERCASE values hide the actual values)

to which the response is a 400 error.

  data: {

      errorCode: 'E0000021',

      errorSummary: 'Bad request.  Accept and/or Content-Type headers likely do not match supported values.',

      errorLink: 'E0000021',

      errorId: 'oaeEf5o-pigQ0Cqtj6gey4rCA',

      errorCauses: []

    }

Looking at the message about the Accept or Content-Type headers, I checked what was being sent:

 'Accept: application/json, text/plain, */*\r\n' +

 'Content-Type: application/json;charset=utf-8\r\n' +

Note that these values for Accept and Content-Type headers are unchanged from what was being sent to the old 'idfed' endpoint.

The only changes to the new endpoint were copying the API Key and getting a new client secret per the instructions on migrating to the new endpoints, encoding these in the Authorization header, changing the URL and adding the state and nonce query parameters. 

Any thoughts on what might be the issue? 
I've been following these instructions: