What a great question! This subject area can be confusing because there are so many different technologies and options. As you point out, so many of them fail your particular requirements.
Local Distributed Storage - Continuous File Synchronization
As I understand your needs, you have several people each working on their own local hard drive containing TBs of data. But you want it to work AS IF there is just one hard drive that is always the same for everyone and is local. If one person adds or changes a file, all users have that new file or change (almost) immediately on their local hard drives.
ViceVersa Software - $49.95
I believe ViceVersa software from TGRMN Software will do this for you:
At $59.95 per user ($49.95 each for 2-5 users) it certainly is affordable. It is limited to MS Windows. (I have no financial interest in TGRMN, but a strong interest in over-the-Web synchronization and backup.)
It is truly decentralized. You set up your WAN, presumably a VPN. (But see a simpler option with PogoPlug, below.) On each PC you set up which directories you want to bi-directionally synchronize. I believe you want to set it up so that the newest file overwrites its older, unchanged counterparts. ViceVersa is smart enough that if a file changes on both Source and Target, you reconcile the conflict manually.
File Conflicts with Synchronization
File conflicts are potentially a big issue in a decentralized, synchronized world. You need to make smart choices about how to handle deletes. If you delete a file, do you want it deleted from all other PCs? If someone else was working on a document and you delete it before they save it to disk, what do you want to happen? I believe ViceVersa gives you all the options, but you need to understand their effect and choose wisely.
I am curious about this situation. Assume you have a Docs folder on each of three PCs on your WAN: A, B and C. You have continuous bi-directional synchronization set up between Docs on A and Docs on B. The same sync is set up between B and C. And the same for C and A.
Now you add a file to Docs on A. Let's say it syncs first to B and slightly later, due to a slower connection, to C. So now B tries to sync the file to C but let's say C already got the file and is about to sync it to B. It is really important that B and C each recognize that they each have the same file and DON'T need to sync it.
You can avoid any potential issue arising from these three-way connections by using a PogoPlug or other device as a hub.
Using ViceVersa with PogoPlug or NAS as a Hub
Here is an option that may be of interest if you want to avoid the complexities of setting up a VPN and setting up synchronization between each pair of computers. You can make a large USB drive and even multiple USB drives plugged into a PogoPlug appear as drive letters on all of your individual PCs. (Amazon has good pricing, around $80, on PogoPlug.)
Set up ViceVersa on each PC so that it synchronizes with the P: drive, the USB drive on the PogoPlug. The drive just acts as a go-between. You could do the same thing with a NAS device, but the PogoPlug is amazingly simply to set up and connect to. Any one of your users could host the PogoPlug by connecting it to a port on their cable modem or switch. You do not need to have a PC up and running for the PogoPlug to be available. It does not connect to a PC but straight to the Internet.
Aspera has a good image showing this configuration, but instead of a big server at the center, imagine a $79 PogoPlug and multiple TB USB drives at the center:
I came across a few potential alternatives, but none as promising, simple nor as affordable as ViceVersa and PogoPlug.
Terrible website, at least in FireFox
By the way, this is my first post on Super User. I hope others find it useful and vote-worthy despite its length!