I figured almost all of this out.
The short of it is, if you want the Fitness app to show you only One Ring, i.e. the Move Ring, you need to make sure that no Apple Watches are associated with your iCloud account. This however is harder to do than one would imagine.
The problem is that you can't have any Apple Watches associated with your iCloud account. I had tested AWs before, but I don't currently have one. But my wife has one. But it's under her account. Or so I thought. She, and everyone else in the family have their own iCloud accounts, but are all logged in to my account for the AppStore. I've had it this way for a decade plus. Well, it turns out that when a device, like her watch, is logged into my AppStore account, it then shows up under my devices under iCloud. So the solution was to remove her watch from the list of "my" devices under iCloud (you can do this on phone or Mac, just click on your name in settings, and you'll see a list of all of "your" devices, which in my case is every device everyone in my family (kids, parents, etc) own).
This unfortunately creates another problem whereby, now her watch keeps asking for the password to my account bc it is trying to update the apps on itself, and the second you input that password, the watch gets re-added to my iCloud account. So the only solution is to log her out of my AppStore account on her phone, and log her into her account. And then share my app purchases via Family Sharing, which I do already have set up. But then, as I understand it, you either have to delete all the apps on her phone and redownload them under her account, otherwise, they will keep asking for my account password in order to update, and when you provide that password - catch 22 - the phone/watch gets re-added to my account.
I'm open to any ideas or suggestions.