Just go TG direct. It's really silly to spend an extra 12 hours. I wasn't that impressed with OZ F that on an upcoming trip I'm opting for BR J for LAX-TPE-BKK instead of going through ICN in F.
The most back tracking I've done is JFK-TPE-NRT but that was an award to do my first Royal Laurel flight AND try one of the Hello Kitty planes.