Just add the ECR images using image: {aws_account_id}.dkr.ecr.{region}.amazonaws.com/{your-repo}:{your-tage} (everything in curly brackets must be replaced with their correct value) and make sure you used docker login before. Since the ECR credentials are only temporarily valid, you will have to repeat this command whenever you open a new terminal - for other private registries this is usally cached for as long as you logout from the registry again).
The docker compose command lacks the equivalent of docker-compose pull. It appears that at the moment indeed it is not possible to update images that point to a mutable tag.