How to get around BinaryMediaTypes CloudFormation bug

cloudformation.yml

ApiGatewayLambdaProxy:
    Type : AWS::ApiGateway::RestApi
    Properties :
        Name : !Ref AWS::StackName
        Description: "Single Lambda proxy"        
        # BinaryMediaTypes: - this is broken in CloudFormation on create
        # - "application/protobuf"
        Parameters:
          endpointConfigurationTypes: EDGE
        Body :          
          swagger: "2.0"
          info:
            version: "2018-01-23T15:50:43Z"
            title: "Lambda Proxy"
          basePath: "/prod"
          schemes:
            - "https"
          paths:
            "/{proxy+}":
              options:
                consumes:
                - "application/json"
                produces:
                - "application/json"
                responses:
                  "200":
                    description: "200 response"
                    schema:
                      $ref: "#/definitions/Empty"
                    headers:
                      Access-Control-Allow-Origin:
                        type: "string"
                      Access-Control-Allow-Methods:
                        type: "string"
                      Access-Control-Allow-Headers:
                        type: "string"
                x-amazon-apigateway-integration:
                  responses:
                    default:
                      statusCode: "200"
                      responseParameters:
                        method.response.header.Access-Control-Allow-Methods: "'DELETE,GET,HEAD,OPTIONS,PATCH,POST,PUT'"
                        method.response.header.Access-Control-Allow-Headers: "'Content-Type,Authorization,X-Amz-Date,X-Api-Key,X-Amz-Security-Token'"
                        method.response.header.Access-Control-Allow-Origin: "'*'"
                  passthroughBehavior: "when_no_match"
                  requestTemplates:
                    application/json: "{\"statusCode\": 200}"
                  type: "mock"
              x-amazon-apigateway-any-method:
                produces:
                - "application/json"
                parameters:
                - name: "proxy"
                  in: "path"
                  required: true
                  type: "string"
                responses: {}
                x-amazon-apigateway-integration:
                  uri: !Sub
                    - arn:aws:apigateway:${AWS::Region}:lambda:path/2015-03-31/functions/arn:aws:lambda:${AWS::Region}:${AWS::AccountId}:function:${LambdaName}:${Stage}/invocations
                    - { LambdaName: !Ref LambdaName, Stage: !Select [ "0", !Split [ '--', !Ref 'AWS::StackName' ] ] }
                  responses:
                    default:
                      statusCode: "200"
                  passthroughBehavior: "when_no_match"
                  httpMethod: "POST"
                  contentHandling: "CONVERT_TO_TEXT"
                  type: "aws_proxy"
          definitions:
            Empty:
              type: "object"
              title: "Empty Schema"
          x-amazon-apigateway-binary-media-types:
          - "application/protobuf"