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Hmm. I do agree with the above.
I WAS in the SAME EXACT position for you. Except for the fact that i Used CX web, cancelled then rebooked through a TA ( who saved me a lot) (SQ was cheaper). Call CX and say I want to cancel and then rebook. Rep told me that there is no fee if you rebook the same exact itinerary. I did it, still waiting for payment to show up. Saved about $300 pp.
So yeah. Make sure you tell the rep that there should be no fee.
ask me If you need any more help.