You could also use the SBB's Fly Rail Baggage service (CHF 22 per piece of luggage) to have it delivered to the closest rail station.
http://www.sbb.ch/en/station-service...l-baggage.html It would take a day or two for the luggage to arrive at the station, but then give you time to take the other pieces back and collect the rest later at the designated station. Perhaps you could manage the 2 suitcases and carry-on on the train/tram and then check the bike? Good luck with everything!