I thought there was something to this article until I hit the Lambda section and realized that you were misusing Lambda as opposed to putting your REST API on API Gateway as that is where it should be defined.

Then I rolled up and realized that you weren't using Kinesis fanouts which would resolve your problem entirely. That said, EventBridge is more likely the appropriate architecture for what you're trying to build as opposed to Kinesis.

For CloudFormation you probably should be using CDK - though I'm confused by the lack of drift detection because that is a fundamental feature of CloudFormation.