Class of travel?
Other than SQ SYD-SIN-MAN-IAH what you found?
AA AS & BA have many common ff partners, so options with those may be limited.
BA fly SYD-SIN-LHR. Fewer options from AKL, but CX fly AKL-HKG
AS awards allow stopover, but award chart is restricted
Easter is 19 - 22 April and is a busy time for travel