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Sorry for the delay, but I wanted to check into this before replying.

I don't know whether I'll be able to help here. I currently have one site in my control with multiple users. Access for profile pages was already turned off for all but the top administrators. (I assume you're talking about the "access user profiles" permissions at admin/user/permissions.)

Enabling the above permissions and running a search for a user name as an anon user, the search returns pages in which that user's name appears, but not user profile pages. (I can, of course, access user profile pages directly via the appropriate paths, with the above permissions enabled.) 

Those are the same results when I run the search as an admin user (no surprise, as I've now enabled equal permissions for both). Either way, they're the same results I would expect without any "access user profiles" permissions enabled.

In your case, what result do you get when you DO have access permissions for user profiles enabled? Does search for a user name return a list of content in which the user's name appears, plus the user profile page? Or are you somehow getting a listing of content submitted by that user? I don't get anything like that, so I wonder what you are getting.

In any case, if you are getting the search results you want when you keep access for profile pages enabled, is there a reason why you don't keep access enabled?

Also, is there a way to get the results you want using Views? I'm sure a View can return a list of all content submitted by a user. (Anyone out there have experience building such a View?)

Finally, I think I saw that you posted this question to the drupal.org forums too, but I didn't subscribe to the thread. I'd like to follow it; can you post the thread URL here?