Ask HN: No-fixed-cost container service/microservice setup on AWS

What architecture are folks using to get a no-fixed-cost set of microservices running on AWS for containerized services.

Essentially, I want to run an auto-scaling set of containers backed by a single image fronted by a fixed IP address and port(s). However, I do not want to pay a fixed monthly charge, just a charge that is proportional to usage.

API Gateway + Lambda does this, but not for containers/images.

Fargate looks promising, but it appears that you need a load-balancer to give the service a static IP which costs $20 or so per month/fixed.

Some combination of Route53/AWS Service Discovery/API Gateway and Fargate might also work, but it is unclear how to set that up.

Does anyone have something that works for them?