Use an existing EBS volume with the Docker REX-Ray plugin on ECS
I found the issue.
The problem is the "scope" property. The docs had the following to say:
The scope for the Docker volume that determines its lifecycle. Docker volumes that are scoped to a task are automatically provisioned when the task starts and destroyed when the task stops. Docker volumes that are scoped as shared persist after the task stops.
So, I just had to change it to "shared" from "task" to make it use the existing EBS volume.