How sick would you like the automation? I would probably take a day and write a python script to do everything for me:
(1) For each source (harddrive), build a list for which each entry contains the filename, md5 (or another hash), size, and modification date (and other criteria you would like to use).
(2) Use python sets to find out which filenames exist across all sources and make one list containing the files that exist across multiple places.
(3) For those files in that list, automatically copy all files to the new place with different filenames and append modification date to filename or number them (e.g., 2015-03-20 == #1, 2015-05-30 == #2 etc).
(4) Copy the rest over.
Or am I missing something?