Hello Courtney,
I have the autosave option disabled but the "automatic saving on render end" enabled. Since the latter creates the filename via timestamp it will never be overwritten. So I can render several scenes, regions etc. on one system and have all the files ready. Only downside is that the file will be saved locally and not on a network.
It's not entirely what you are looking for, but could still help you out! At least until there is a better solution.
Best,
Ararat