You should really only have one primary usergroup, that being "registered" where everyone with a confirmed account has a base set of permissions.
As noted, the original setup was done by another. I believe that "registered" indeed has a base set.
Any other group assignments should be as secondary groups. If you don't do that, then you're not really using the permissions system as it's intended to be used, and this can mean anyone who tries to help you troubleshoot this is coming at this from a completely different angle.
Understood. The angle of approach is part of this, I'm coming in on an unknown heading
You can hamstring the permissions system if you want to, but you need to be clear that you have done so.
I get that. To this green hand, the permission system remains mysterious. And again, I'm coming late to the party. For one thing, all I have done thus far is try to promote a member to mod, which worked except that his access to two nodes vanished. I do NOT think that the original setup deviated from standard as far as permissions goes.
Do a series of "search for users" via ACP and search only by "primary user group" and go through each usergroup and see if you have anyone with anything other than Registered or Unconfirmed as their primary group. Let's start there.