Well, I tought one of the developers would easily confirm the problem which was why I did not provide more information -- my bad.
Turns out that on my server, PHP was setting $_SERVER['SCRIPT_NAME'] to '/php/php.exe' rather than what it was supposed to be: '/zenphoto/index.php'.
Once I fixed that zenphoto appears to run fine in a subdirectory.
My apologies for the false alarm.
Please consider this thread dead. Thank you.