Through experimentation with brian.mccarthy, we've found that EBS volumes only come back up with the amazon1-2018-test Evergreen distro if the entry in /etc/fstab uses the UUID of the drive. The ubuntu1604-powercycle Evergreen distro doesn't appear to be impacted. Note that this is also the recommendation in Amazon's documentation as well:
To mount an attached EBS volume on every system reboot, add an entry for the device to the /etc/fstab file.
You can use the device name, such as /dev/xvdf, in /etc/fstab, but we recommend using the device's 128-bit universally unique identifier (UUID) instead. Device names can change, but the UUID persists throughout the life of the partition. By using the UUID, you reduce the chances that the system becomes unbootable after a hardware reconfiguration. For more information, see Identifying the EBS Device.
Based on https://unix.stackexchange.com/a/270216, we can use either the blkid -o value -s UUID /dev/xvd... or lsblk -no UUID /dev/xvd... command to get the UUID and write that in place of $device_name in the mount_drives.sh script.