Help changing ticket segment
So I'm flying PVG-HKG-JFK-HKG-PVG.
I'm currently booked PVG-HKG on KA 865 (CX ticket), and HKG-JFK on CX 846.
I want to change my flight PVG-HKG to a CX flight (that's 20 minutes earlier, CX 367), but when I do it online and when I call in, they say they can't change it before they have to reissue both segments and my second segment (HKG-JFK) is fully booked.
I've checked and there is availability in my booking class, and there are plenty of seats available (in both segments).
I often change my tickets last minute and this is the first time I've had an issue.
So what can I do at this point? I don't know if it really can't be changed or a case of lack of know-how of the CX ticketing office agents.