So, lovely.
tdw’s suggestion had me thinking. So I updated the file and still an error. Oddly enough, the idea of permissions struck me. Some php files seem to be kosher with 6xx (which seem to be the standard permission sets). _HOWEVER_ when I randomly went ahead and changed the permission (to cheat, I just changed it to 777, but I’m sure 755 will be sufficent) on related_posts.php and, lo and behold, no more errors! Sure enough, doing the same to the other problem files, makes everything work. So the answer to my question all comes down to permission errors. Yay!
WordPress still rocks, thanks for the help.