Specify Destination ARN for API Gateway Custom Access Logs?

We deploy multiple serverless services to a shared api gateway—we would like custom access logging to be turned on, as so:

logs:
  restApi:
    accessLogging: true
    format: 'requestId: $context.requestId'
    executionLogging: true
    level: INFO
    fullExecutionData: true

However, the Access Log Destination ARN changes every time a service is deployed (generated from the service name), whereas we would like to point the entire gateway to one shared log group. Can this ARN be fixed as part of this configuration like the format or log level can be?