I had the same issue with changing a Lattiude fare for 1/2 used trip returning to London. When I checked online, the website showed an option which would have worked on my revised date and it was $60 less. Except, I could not make the change online. I had to call in. When I called in, the agent said, like you it was $600 fare change. I challenged him on it, and said it was $60 REFUND doing it online. He checked the website and saw what I was seeing. Eventually after a few being placed on hold, he said something like “The B fare class is not available on my flight”, after some more being put on hold, he returned with , OK I can change you to the new date, but I would not get the $60 refund. I was ok with that and accepted it.