I was under the impression that AUFS was not preferred since it is not expected to become a standard available component in Fedora linux distributions (http://developerblog.redhat.com/2014/09/30/overview-storage-scalability-docker/).
Switching the storage type we configure Docker to use is certainly an option for us, as long as the alternative(s) address the problem and are stable and readily available for CentOS. This is for our production environment.
The frustrating thing is that others appear to have had success resolving the issue by upgrading (https://github.com/docker/docker/issues/3182#issuecomment-70704879), but we are still seeing the problem behavior on CentOS 6.6 and CentOS 7.