If using the Garmin API reduces the bottleneck from strava then I think this is a great idea!
One note on the implementation - I would not want to lose the Strava activities already added to my life map if I started to sync through Garmin instead of Strava (many of my activities linked to my lifemap from strava were not recorded with a Garmin device).
Perhaps a user’s Strava account could remain linked to citystrides, but syncing could be paused indefinitely (maybe through a simple user control). This would keep all the users previous Strava activities synced. All future runs would then be uploaded to citystrides through Garmin.