Here are some options to Bangkok (same date as above and again, from ORD, as you will have to find an AA flight from MCI to ORD and have them lump it in your itinerary when you call to book)
Outbound
Chicago - Bangkok - Saturday 2 March 2013
Search up to 7 days earlierSearch up to 7 days later
Depart
Arrive
Flight Operating Airline
Class of travel
10:15 2 Mar
ORD
14:30 3 Mar
NRT
Japan Airlines
JL0009
Economy
Only 4 reward flight seat(s) left in this class
18:05 3 Mar
NRT
22:40 3 Mar
BKK
Japan Airlines
JL0707
Economy
Only 4 reward flight seat(s) left in this class
1 flight connection, total journey time: 23 hours 25 minutes.
Inbound
Bangkok - Chicago - Monday 11 March 2013
Search up to 7 days earlierSearch up to 7 days later
Depart
Arrive
Flight Operating Airline
Class of travel
08:05 11 Mar
BKK
16:15 11 Mar
NRT
Japan Airlines
JL0708
Economy
Only 4 reward flight seat(s) left in this class
18:45 11 Mar
NRT
16:35 11 Mar
ORD
American Airlines
AA0154
Economy
Only 7 reward flight seat(s) left in this class
1 flight connection, total journey time: 20 hours 30 minutes.
23:00 11 Mar
BKK
06:55 12 Mar
HND
Japan Airlines
JL0034
Economy
Only 4 reward flight seat(s) left in this class
11:00 12 Mar
NRT
08:45 12 Mar
ORD
Japan Airlines
JL0010
Economy
Only 4 reward flight seat(s) left in this class
The cost of travel between airports is not included in your fare.
1 flight connection, total journey time: 21 hours 45 minutes.
23:00 11 Mar
BKK
07:10 12 Mar
NRT
Japan Airlines
JL0718
Economy
Only 4 reward flight seat(s) left in this class
11:00 12 Mar
NRT
08:45 12 Mar
ORD
Japan Airlines
JL0010
Economy
Only 4 reward flight seat(s) left in this class
1 flight connection, total journey time: 21 hours 45 minutes.
08:25 11 Mar
BKK
12:10 11 Mar
HKG
Cathay Pacific Airways
CX0700
Economy
Only 5 reward flight seat(s) left in this class
13:00 11 Mar
HKG
15:20 11 Mar
PVG
Dragonair
KA0874
Economy
Only 5 reward flight seat(s) left in this class
18:00 11 Mar
PVG
18:30 11 Mar
ORD
American Airlines
AA0288
Economy
Only 7 reward flight seat(s) left in this class
2 flight connection, total journey time: 22 hours 05 minutes.
There were more options outbound the next day and you can play with different weekends to get the flights and time you want. On this particular day there wasn't Cathay availability outbound but they were available the next day and probably various other saturdays in your timeframe. that's probably about as close as you are going to get via One World airlines. But you should be able to hop a Thai Airlines flight for pretty cheap from there. Unfortunately Thai is a Star Alliance partner so you can't add it to the end of this itenerary. If you have US Air or United miles you could use them on the Thai Airlines flight but it will probably be reasonably priced. Bangkok air is the other carrier that flys there. here's the carriers and where they service from:
Bangkok Airways Bangkok-Suvarnabhumi, Chiang Mai, Hong Kong, Krabi, Kuala Lumpur, Pattaya-U-Tapao, Phuket, Singapore
Firefly Kuala Lumpur-Subang, Penang [begins 11 August 2012]
Silk Air Singapore
Thai Airways International Bangkok-Suvarnabhumi