OP - Are you trying to force a cancellation here??? rather than taking whatever rerouting is offered (given you assumedly have other segments)
If so I suspect any refund will be low (as per single fare pricing) and probably paid by CX only - I can't imagine CX has an easy way of splitting any refund across the remaining segments and carriers.
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My only experience with CX on a semi-similar is on an ex-TPE J Class Business Saver TPE-HKG-xSYD-xHKG-TPE. Cost was about US$1500. Stopped over at Sydney and was unable to get leave for return flight within six months. Ticket cancelled and refund was US$200 which was explained to me as difference between my fare and a one way fare at time of ticketing. Admittedly it took 3days for them to work this out and they just refunded with no paperwork or anything (at the time I was ok with it as I frankly was expecting to get nothing back)