See route=ski

Okay, how about this then?
I remove the names from the tracks (particularly between Olympus & Cockayne).
I then create OSM "Route(s)" as relations incorporating those tracks. The Route can have a name such as "Cheeseman - Olympus Traverse".
This way, it would actually be possible to have multiple routes along the same paths, and also e.g. have a separate route for e.g. ski-touring.
I.E., one could also e.g. create a Route for the Canterbury Haute Route ski-tour between Craigieburn & Olympus using the same paths.
What do you think?

Thanks for the feedback/discussion, it's been useful.
Do you object if I simply remove the names from these tracks, as it doesn't feel there is a consensus on names; I'm not aware of these names being used (e.g. by DoC or others) other than as a description.

Fair point, my deletion was ill-considered, my apologies. I have reverted my changeset.
Am still uncomfortable with having these as named "tracks" though. The implication of having some of these (particularly the ridgeline ones) marked as "gravel" "tracks" with names is that there is something there on the ground for the unwary to follow. Personally I see no value in e.g. the Cockayne Descent track on OSM. Why that line down the scree as opposed to any other line off Cockayne? Where does one draw the line in terms of adding paths to OSM? Just feels like a slippery slope... ;-)

They may be commonly used "routes", but there's no/little track on the ground. I disagree that the intent of the highway="path" tag or any track-related tag is for "routes" like these to be in OpenStreetMap, sorry.
I understand your POV differs.
Likewise I disagree that the Mt Lyndon route, or the Lake Lyndon->Trig M route, for example, should be on OSM, but I'm not going to start/continue an argument on it.
Best wishes, happy tramping...