To close out this topic with my resolution, I ultimately just had to simply delete entirely and recreate the page, which wasn't too big of a deal at this point since the site is in development. Still, in terms of restrictions on posts or categories, I remain pretty mystified since it wasn't a post (it was a page), and it didn't have categories or tags.
The only thing I can think of, now that I look at it again, is that in URI restrictions, I added "/members/", but I did that simply because it was listed within the S2Member description itself as an example of what you would use for URIs with BuddyPress.
P.S. If I take off restrictions for /members/ in URI restrictions, the page is fully accessible for the logged-out public despite /members/%%current_user_nicename%%/profile/ being part of my special redirection URL in the login welcome page.