I have had no problem changing tickets booked in U or J classes whether completely unflown or partially flown, subject only to the change fee and most importantly availability. If the desired date/flight does not have availability in the original class, you will have to upfare to an available class or choose another date/flight.

There are times when the flight is completely sold out and so you do not even have the option to upfare. For clarity, it is upfare to revenue FA (first) or ZC (business) classes.
​​​​​​
Have they tried to wait-list for Z class? Sometimes Z availability will open up in the lead up to the flight because other passengers cancel or change their flight.

​​​​​
​​​​