The only places with run-specific routes are NY and Watopia.
Weirdly enough, those are the only ones you get credited for when you run. You can run anywhere, you can complete (multi-use) routes you haven’t done before - but you only get credit for those badges if you cycle them. I’ve tried!
In your list you do have both Watopia and NY routes - Couch to Sky, Hudson Roll, Shuman trail, Park to Peak are all in NY.