ClickOps #18 - Deploy API Gateway Logging

I always want everything to be Infrastructure as Code (IaC); however, that is not always possible! While I can create the API Gateway Role for writing logs to CloudWatch, I do not have a way to perform the one-time configuration per region using the Cloud Development Kit (CDK).

The API Gateway for HTTP has an issue with the CDK constructs on the automatic $Default stage for the logging configuration.