I think this would take an overhaul of the Thread Tag Administration and some of the back end as well. IE instead of having a minimum rank to view/post/moderate, maybe have each rank listed and have check boxes in each of those columns to give permission to view/post/moderate similar to CHMOD for file systems.
This has actually been a plan for a while, but overhaul to support such a system is definitely not trivial. I completely recognize the need for a system of this type, but I simply haven't had the time to make that kind of change, unfortunately
That said, I realize I never answered your original question regarding the private thread tags. When you're logged into your site, do you see these options when you click "My Private Tags"?