In addition to the "free cancellation within 24 hours" there is also a (less documented?) free changes within 24 hours rule. I did this recently when I booked a flight and then within a couple hours needed to change the return date.

I called and asked if I could change it, otherwise I would cancel the original and just re-book. They said that within 24 hours you can just pay the far differential (if any) without triggering the change fee.

So I would book the Y, then call them up within 24 hours and pay the difference to the C. My situation wasn't exactly the same, but the same rule SHOULD apply to your case.