You need to bear in mind that the BA award would be SINGLE partner only - that also means your stopover pretty much limited at either NRT- HKG, or NRT- SIN - KUL if this is JL you use; or HKG-BKK-SIN, or HKG - DPS if this is CX you use. I am not even sure CX flies BKK to SIN.

BA's stopover is not as people led to believe by bloggers that are "unlimited" - it has to be at "natural connection points en-route"... Since you are limited to either JL or CX - you dont get to fly the way you imagine.