@quokka that's an interesting take and I never thought about that. However, I think if the group appears in or is searchable by users that are not in the group, that'd be a no go for our users.
I also realize now that my above statement is inaccurate. If a member navigates directly to the URL of a hidden and private group then they are able to view it. As an intermediate measure, I've trained our moderators to pass these links around so that group members can still get to their group pages. And if the person navigating to the user is marked as a group owner, they are able to navigate to the group page.
The only issue that remains for my use case is a user finding hidden/private groups that they are in.
If I get some time, I'll look into the code to see if there's a way to populate these groups into user profiles as a list or visible in the group listings/search for members. And if that's of interest to the community here, I can share it back through PR to NodeBB or whatever is preferable.