AWS EBS I/O Bottleneck
We have had this answer back from AWS Support which shows where the bottleneck is occurring:

If you would like to reach 250MB/s, the maximum throughput of r3.4xlarge, you can change the volume to Provisioned IOPS(io1). IO1 has maximum throughput of 320 MiB/s. Another approach is to build RAID 0 array with 2 gp2 EBS volume. You can see the guidance from link [2].