I've had similar issues on award connections, once you have flown the first segment it is probably impossible to get changed via flying blue (since the only way they have to change is cancel refund miles and rebook again).
However, once agents understand this and also understand that per the rules it should be possible but the process is messed up they CAN if they WANT TO use their empowerment to reroute you as INVOL working as a team around procedures in your favor. This is what then happened to me in the end, was just rebooked free of charge for example because the later flight was more full or because of a family emergency or wahtever they documented in the system to make it plausible and make it happen. This is really also soemthing where it pays off to try different agents and know their ways of working.
Sorry it was such a mess. It shoudl not be, indeed.