Honolulu - Singapore flights

There does not appear to be direct flights. I used a date in Feb 06 with Expert Flyer and got the following, but all with one connection

6 Flights Returned

1 Connection
BR 21 0 HNL
02/03/06 12:10AM TPE
02/04/06 06:00AM 332
SQ 29 0 TPE
02/04/06 07:15AM SIN
02/04/06 11:50AM 772

1 Connection
BR 21 0 HNL
02/03/06 12:10AM TPE
02/04/06 06:00AM 332 M C0 J0 Y0 K0 T0 L7 B0 V7 R7 U0 H0
BR 225 0 TPE
02/04/06 07:40AM SIN
02/04/06 12:00PM 332 M C4 J4 Y7 K7 T0 L7 B0 V0 U0 R0 H0

1 Connection
UA (NH) 9719 0 HNL
02/03/06 10:15AM NRT
02/04/06 02:45PM 763
NH 901 0 NRT
02/04/06 04:25PM SIN
02/04/06 10:50PM 777

1 Connection
UA 833 0 HNL 02/03/06 09:45AM KIX 02/04/06 02:55PM 777
SQ 983 0 KIX
02/04/06 04:35PM SIN
02/04/06 10:35PM 772

1 Connection
NH (UA) 7057 0 HNL
02/03/06 09:45AM KIX
02/04/06 02:55PM 777
NH (SQ) 6265 0 KIX
02/04/06 04:35PM SIN
02/04/06 10:35PM 772

1 Connection
NH 1051 0 HNL
02/03/06 10:15AM NRT
02/04/06 02:45PM 763
NH 901 0 NRT
02/04/06 04:25PM SIN
02/04/06 10:50PM 777

 

There are no direct flights on *A airlines (I checked the *A routing map). Another option is maybe using Korean Air via ICN :?: