chriswhy
I saw the "download relation" button in iD, which does allow one to split the path. Still, this 18.5 mile path has many points in which it splits off into two separate paths, sometimes with just a narrow bit of grass between them and sometimes quite more distance. Here are the two relations:

Bike route: https://www.openstreetmap.org/relation/17527976

Foot route: https://www.openstreetmap.org/relation/8676789

Deleting large segments could be an issue with deleting a lot of history:

https://wiki.openstreetmap.org/wiki/Keep_the_history

That page brings up JOSM as a method of bringing the history of an old segment into another one using "replace geometry". However JOSM performs very poorly for me when working with a large data set. I'll see if I can figure out how to download only the path, unlike before.