Hey Kevin,
I'm sorry that you are having all this trouble, but as far as saving to the root directory, I get this error dialog when I try to do so.
Like I said, it has been that way for as long as I remember, so I'm thinking that your problems may lie elsewhere.

Knowing that I can't save there I have always saved the project I am currently working on to the desktop.
I just tried to save a file to the root directory of my 2 other attached volumes, and got the same error dialog.
However if I created a new folder in the root directory of any volume I am able to save to those new folders.

It definitely sounds like you have a permissions problem though, you should always be able to save into any folder inside your "Home" folder.
A clean install of Sierra should have reset the default permissions, but I'm not 100% sure since it mostly overwrites the system folder permissions, and not the user's folders.

I do know that the ability to repair permissions, was removed from Disk Utility in the last few versions of OSX.
I have used Onyx, to repair permissions since Apple took it from disk utility, with good results.
Maybe it would be worth a try to see if Onyx, could possible restore permissions on folders other than the system folder.
https://www.titanium-software.fr/en/onyx.html

Just be sure to download and use the exact version of Onyx for the system software version that you are running.
Hopefully this is of some help.

- Jay

MacPro 5,1/12 core@3.46GHz -- OS X 10.15.7 -- ATI 7970 -- 32 Gig RAM -- Crucial 500GB OS SSD -- Samsung EVO 1TB Audio/Sample SSD -- BIAB 2024 -- Logic Pro X -- Cubase Elements 14 -- Too many plugins