Sitewide Privacy defeated by Recent Sitewide Posts

I set up a totally private blog using Sitewide Privacy. It worked fine, required password entry, etc.

I did a Welcome Post. Later, on my main site, I looked at the Posts listed by Recent Sitewide Posts and, to my horror, there was my private Welcome post listed.

Posts within the private blog can be made private IF all members remember to do Quick Edit and check the Private Box. However, this is tricky because all members are not exactly geeks.

Is there anything I can do in the admin setup to insure that all posts done in my private blog automatically have the Private Box checked or have privacy set in some other manner?