How much does it matter where you put your Google sitemap in the directory? Can it be anywhere if you let Google know where it is through webmaster tools? Of course it needs to be in a public folder.
Google say to put it in the root, so that is pretty much where is must stay. Dont forget to submit to Bing and Yahoo as well!
Upload your sitemap.xml to the root of your website then submit the url to your sitemap with search engines.