On May 31st 2014 I completed a solo loop around Rapa Nui (or Easter Island): 65.05 kms, 9hrs 5mins. And I think it stands as 'unsupported' - unless you count the little black dog who accompanied me for about 20miles - and the 2 glasses of rainwater I gratefully accepted along the way!! 

PHOTO 1: View of the southern coast of Rapa Nui and the site 'Tongariki' - in the middle of the pic is the crater of Rano Raraku (moai carving centre) - and also, in the foreground, my canine companion. 

This site has some info: https://besthike.com/s-america/patagonian-andes/cerro-castillo/

The 130km Huayhuash Circuit circumnavigates Peru's Cordillera Huayhuash. It is widely considered to be one of the top treks in the world. It includes numerous passes over 15,000' and up to 16,500'.

Here's a nice article about Choquequirao & the planned "improvements" to get more tourists in.
www.theguardian.com/travel/2014/nov/01/peru-choquequirao-inca-ruins-trek