Suggest adding a source data timestamp parameter to set as the copy point in time for AzCopy operations.
Adding a /SourceDataTimeStamp parameter would allow for the ability to only copy data that is at that timestamp or earlier from the source data to the destination. For example, I have many tables and blobs that tie to each other. When I back them all up in a live hosted system, it would be great to say "AzCopy, copy all table and blob data from 2017.09.02 and earlier to another location". This would ensure that if I later restored from that time point, all the data would be be linked up properly.