Sure! Conflict Catcher was a great tool.
Of course we needed great tools back then. Today things are just supposed to work, and for the most part they do. But when they don't, troubleshooting is not as simple as it once was. Your technique is a good one and no, you're not risking anything remotely disastrous. I was going to suggest it. You just have to do things methodically, with patience, and with a backup / recovery plan already in place.
The likelihood of finding a "smoking gun" is remote though, if for no other reason that so much of what used to be under local control is now delegated to the maddeningly opaque and seemingly capricious iCloud. If Safari is one of the many iCloud services you are using, it can definitely be a contributing factor.
You might also consider creating a new, temporary User Account to determine if it exhibits the same behavior. That might implicate a macOS / Safari problem that only Apple can fix, or it might justify additional troubleshooting "local" to your Mac. If iCloud syncing could be a factor, you could try using a different iCloud Account for that temporary User Account.
By the way I tried and failed to replicate what you're seeing. If I make a change to Website Preferences they stick, and as you already know that's what should be happening.