I'm thinking the files might be on AWS. There was a huge pentagon leak about 3 years ago:
https://www.upguard.com/breaches/cloud-leak-centcom
I also saw read some robby mook emails referencing aws, around general #1650 or so.
It appears at least part of their infrastructure involves Cisco. I'm not an IT guy, so feel free to weigh in.
If your theory is correct, then AWS is the most likely souce, hands down. They host almost everything for the federal government. At one point I had to use it to draw data on nonprofits from the IRS. If there is an open bucket out there with government info, it will be somewhere on their cloud.
They found the open "buckets" by doing a search of *com. I don't think it will be that easy for us. Good chance we'll find clues in Q's posts:
I won't have much time to help look until next week, but hopefully this gives you some ideas.