Korean Air Skypass - Booking Korean Air Flights

I'm trying to book the following flights...

9/18/2011 JFK - ICN
9/20/2011 ICN - AKL
10/2/2011 AKL - ICN
10/2/2011 ICN - JFK

In a fare class that I'll be able to earn Skymiles on.

Class Exclusions Are: A, B, D, G, N, Q, U, V, X

Korean Air's website shows only "Q" fare. I believe I need an "S" for that flights or the cheapest fare that's not in the excluded list above.

Suggestions?

Currently on JFK AKL routing, KE is offering Q and S fare.

Q fare is USD1620+tax
S fare is USD2070+tax

If you're not seeing the higher fare on KE's site, then the only way to book "S" fare is call them directly or contact travel agency.

Any Suggestions on where i can book an S fare online?