AWS SAM template - set Integration response mapping template

I have a AWS SAM template that creates a API Gateway hooked into a Step Function.

This is all working fine, but I need to add a Integration Response Mapping Template to the response back from Step Functions.

I cant see that this is possible with SAM templates?

I found the relevant Cloud Formation template for it: https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/aws-properties-apitgateway-method-integration-integrationresponse.html

But It looks like I would have to create the whole AWS::ApiGateway::Method / Integration / IntegrationResponses chain - and then I'm not sure how you reference that from the other parts of the SAM template.

I read that it can be done with openAPI / Swagger definition - is that the only way? Or is there a cleaner way to simply add this template?

This is watered down version of what I have just to demonstrate ...

Transform: AWS::Serverless-2016-10-31
Description: My SAM Template
Resources: 

  MyAPIGateway:
    Type: AWS::Serverless::Api
    Properties:
      Name: my-api
      StageName: beta
      Auth:
        ApiKeyRequired: true 
        UsagePlan: 
          CreateUsagePlan: PER_API
          UsagePlanName: my-usage-plan
          Quota:
            Limit: 1000
            Period: DAY
          Throttle:
            BurstLimit: 1000
            RateLimit: 1000
      
  MyStateMachine:
    Type: AWS::Serverless::StateMachine
    Properties:
      Name: my-state-machine
      DefinitionUri: statemachines/my-state-machine.asl.json
      Events:
        MyEvent:
          Type: Api
          Properties:
            Path: /myApiMethod
            Method: post
            RestApiId: !Ref MyAPIGateway

          # TODO: how to we define this Integration Response Template ?
          # IntegrationResponse:
          #   Template:
          #     application/json: |
          #         ## parse arn:aws:states:REGION:ACCOUNT:execution:STATE_MACHINE:EXECUTION_NAME
          #         ## to get just the name at the end
          #         #set($executionArn = $input.json('$.executionArn'))
          #         #set($arnTokens = $executionArn.split(':'))
          #         #set($lastIndex = $arnTokens.size() - 1)
          #         #set($executionId = $arnTokens[$lastIndex].replace('"',''))
          #         {
          #           "execution_id" : "$executionId",
          #           "request_id" : "$context.requestId",
          #           "request_start_time" : "$context.requestTimeEpoch"
          #         }