Have you considered using overlays from route360 (https://developers.route360.net https://developers.route360.net)? They are doing some really interesting stuff

Have you considered using overlays from route360 (https://developers.route360.net https://developers.route360.net)? They are doing some really interesting stuff with multiple transit types (bicycle, car, mass transit, walking) as well as accounting for elevation changes and incorporating GTFS data where applicable.