Here is a SkyTeam option from a non-hub (AUS-MEM-ORD-ICN-BKK-AMS-MSP-AUS). It violates the "leave after 5 pm on Fri" rule but is the best you can do on SkyTeam.

Austin To Seoul, at 11 Sep 2009 ( 7595 Mi ) ( 12152 km )
NW3510 / NW3500 / KE38 Dep 6:00 , Arr: 16:10 Stops: 2 Dur : 20h10m
Northwest Airlines 3510 Dep: AUS at 6:00 , Term: Arr: MEM at 7:48
Equip: CR9, Meal: , Dur : 1h48m
Northwest Airlines 3500 Dep: MEM at 8:50 , Term: Arr: ORD at 10:36
Equip: CR9, Meal: , Dur : 1h46m
Korean Air Lines 38 Dep: ORD at 12:35 , Term: 5 Arr: ICN at 16:10
Equip: 744, Meal: LD, Dur : 13h35m

Seoul To Amsterdam, at 12 Sep 2009 ( 7985 Mi ) ( 12776 km )
KE651 / KL878 Dep 17:35 , Arr: 5:45 Stops: 1 Dur : 19h10m
Korean Air Lines 651 Dep: ICN at 17:35 , Term: Arr: BKK at 21:10
Equip: 773, Meal: D, Dur : 5h35m
KLM Royal Dutch Airlines 878 Dep: BKK at 23:20 , Term: Arr: AMS at 5:45
Equip: 74M, Meal: , Dur : 11h25m

Amsterdam To Austin, at 13 Sep 2009 ( 5202 Mi ) ( 8323 km )
NW41 / NW3633 Dep 10:50 , Arr: 17:18 Stops: 1 Dur : 13h28m
Northwest Airlines 41 Dep: AMS at 10:50 , Term: Arr: MSP at 12:55
Equip: 333, Meal: DS, Dur : 9h5m
Northwest Airlines 3633 Dep: MSP at 14:30 , Term: L Arr: AUS at 17:18
Equip: CR9, Meal: , Dur : 2h48m

Rather pricey in J, though. Over $10,000. And it doesn't quite cross the equator but it is all SkyTeam.