It sounds like Free File Sync is a backup app akin to Windows's own File History, but it makes single copies instead of keeping a record of every change. You only get to restore the last version of each file which is less complicated. Seems to have good reviews, sorry to hear you must pay. I doubt it has a bearing on the issue at hand, unless it is set to sync Win 8.1 files to Win 10 files across the network. But that's what sharing across a network is supposed to do all on its own, I think. Or am I wrong? You know better, really. But, even if it requires syncing, Free File Sync likely isn't the cause of the problem. It is just the canary in the mine that dies first when the network is broke.
I only have an Admin account. I believe a Standard account is safer, but I don't want to be constantly bothered with UACs & lesser user abilities, So, I trust in Windows Security for protection. Also, I keep full system backups in case something does get in & cause real havoc. But neither do I have a Win 8.1 computer, nor even a network. So, I can't say whether the problem would happen to me. I've run this way since 2014 & never got a virus (but I never go anywhere suspect).
(a) Why don't you make your account(s) an Admin for a month -- just to test your theory?
(b) Why not file share through OneDrive one way or another instead of the network?
(c) Have you tried a P2P Network as Kate LI (MSFT) wrote in here...?...
https://social.technet.microsoft.com/Forums/windows/en-US/492f0a6a-13ce-47ea-9118-7922b0c3a50d/windows-10-peer-to-peer-network-setup
Windows 10 peer to peer network setup
Sounds easy enough. Well, get to the Workgroup name this way: "Right-click START, System, System Protection, Computer Name tab"...

I don't know how well it would go or whether it's worth trying seeing as you've got a work around to the problem.