I wonder if it's possible to edit this road so it appears in OSM-based routing APIs? While technically private, it can be driven along with permission, see https://www.mountaineering.scot/access/special-arrangements/strathfarrar

"During the summer season (1 April 2020 to end of October) vehicle access is available to everyone"

Google Maps provides drivetimes here (https://goo.gl/maps/QCghBgdf7yc8Kw9H8) with this warning "This route has restricted usage or includes private roads" and so I wondered if OSM could do the same. I am using the data in OSR - https://openrouteservice.org/