m4.large are very small instances with 2 CPUs if I recall correctly. Try to specify only some larger types such as m4.4xlarge or m4.8xlarge when you create a computing environment, so that Batch will be forced to use only those. Also larger instances have faster network as well, so the container download will take less time.
To have an idea on how much time is spent to download the Docker container you can have a look in the Batch dashboard at how much time the jobs stay in Starting mode. When you have already running ECS instances, and that already staged the container, the jobs should almost instantly pass from Starting to Running state.
Cheers
Francesco