Conflicting Kubernetes CPU usage & Docker Container Metrics
Multiple things here:


Youre on AWS ec2, hence whatever you are doing on your instance for measuring CPU is calculating CPU on hypervisor level and not instance level. To very this run any load test and check iostat -ct 1 and CPU usage in cloudwatch. CPU usage in cloudwatch is always 10-20% greater than what iostat will report and that is because iostat will give CPU usage on hypervisor level.
As docker to see how kubernetes and docker metrics compare i suggest to run the containers with --cpuset=1 or any number to allow all containers to use only a single vCPU.
Also in AWS 1 CPU= 2vcpu. It is hyperthreaded to 2. You can maybe take this into consideration while calculating.
Finally the best metric to use to see CPU usage for a particular application is using htop and correlating with your cloudwatch metrics.
I have also observed sometimes docker daemon pinning itself to one of the virtual CPUs and hence when you are reducing it to 1000m, maybe the whole setup is getting slow because the reduction is happening on any one of the vpcus. You can use mpstat to get into details of this. 
Lastly on the host level you can pin docker to a single CPU and observe more.


Hope this brings you somewhat closer. Update me if you have already found a solution.