ECS does exactly that - it's a (somewhat) managed docker container service, so it would still allow them to run containers.
We should look at ECS though. Are you more likely to deploy if something is in ECS than if it's a straight AMI?
Though I must admit (1) I am not one of your customers, and (2) our BAA with Amazon prevents us from using ECS. We typically run node on ebs backed m3.medium instances running Amazon Linux.