I use Tapiriik to automatically sync things between Strava, Garmin, and Dropbox.
Given that Tapiriik is open-source, it seems like it could be fairly straightforward to add CityStrides as a destination to Tapiriik and/or allow manual uploads from Dropbox, etc.
As a bonus, Tapiriik knows how to avoid synchronizing duplicates and sidesteps the Strava API issue for you.