Is there are a way to use visibility rules to show a block to any user that does NOT have a specific role(s)?
In rules, you could set up the condition to have a role and then check the "negate" box. I'd don't see that option in visibility conditions for blocks on a layout. it seems that I can only create a positive condition for a role. If a user has a role, show this block.
Otherwise, I feel like I am going to have to create a special role just for users that are supposed to see this block.