When I try booking online I see a "Swiss Service Fee" in addition to government taxes, airport fees, fuel surchcarge. I wonder if the fee for using miles is even more?
If I understand you correctly you're trying to use LH miles. Are you booking through Swiss or Lufthansa? I've seen airlines charge different values for the same taxes and the "Swiss Service Fee" might not apply if booked via Lufthansa or might be substantially different or might be a Lufthansa fee.