I'm not totally up to speed on ECS vs EKS economics but it seems like EKS with p2/p3 would be a sweet solution for this. Even better if you have a mixed workload and you want to easily target GPU-enabled instances by adding a taint to the podspec.
ECS GPU scheduling is production ready, and streamlined quite a bit on the initial getting started workflow due to the fact that we provide a maintained GPU optimized AMI for ECS that already has your NVIDIA kernel drivers and Docker GPU runtime. ECS supports GPU pinning for maximum performance, as well as mixed CPU and GPU workloads in the same cluster: https://docs.aws.amazon.com/AmazonECS/latest/developerguide/...