Route: Idaho Centennial Trail (ID)

The 900-mile (1,448 km) Idaho Centennial Trail (ICT) is a scenic trail through Idaho. It winds its way through various ecosystems from high desert canyonlands in southern Idaho to wet mountain forests in Northern Idaho. ICT travelers will cross many mountains, streams and rivers in between.
- via Wikipedia (https://en.wikipedia.org/wiki/Idaho_Centennial_Trail)

The fastest time a search turned up was this 52-day self-supported or supported attempt by Steve Steubner https://www.idahostatesman.com/latest-news/article215773880.html

Notable failed attempts at FKT that were prominent in the search results:
Mat Erpelding: http://www.swxrightnow.com/blogs/outdoors/2013/sep/12/idaho-legislator-goes-hike-bike/
Andrija Barker and Taylor Neal: https://idahonews.com/news/local/friends-nearly-finish-epic-960-mile-idaho-centennial-trail-challenge
Giff Walters: https://rinnanrunning.wordpress.com/2015/06/21/a-magnificent-failure-300-miles-on-the-idaho-centennial-trail/

Giff Walters' research also failed to identify fast successful attempts, as he notes here: https://rinnanrunning.wordpress.com/2015/05/26/idaho-centennial-trail-preview/

GPX source: https://caltopo.com/m/G28M