Allright, Chuck, I managed to fix the issue of all users (regardless of type, registered or not) being able to see and browse thumbnails in all categories (regardless of category permissions) by replacing my pp-inc.php file with the new 7.1 version. I was using a version that dates back to whichever upgrade last stated the need to replace it (which the announcement for 7.1 does not - that file should probably be added to the list). After that change, and that change alone, permissions are now working perfectly.
As a side note, the 7.1 php-inc.php produces a lot more boxes around individual elements in the XenForo style than the previous php-inc did. I cleaned that up by commenting out the 4 lines referring to the XenForo template path and letting my header.htm (tweaked from your demo header.htm) handle that.
As for my cookie problem, that appears to have been caused by my not having "xf_" in my forum cookie prefix field. XenForo now successfully logs PhotoPost in and out... but... PhotoPost still can't seem to do the same for XenForo. Any thoughts?