What I think I did (I tried lots of things!) was:
- Uninstall old version of K4PC
- Install latest version of K4PC
- Deregister my Amazon account from within K4PC settings (removing all current licenced content)
- Re-register my same Amazon account from within K4PC settings
- Sync my archived books
At no time did I do anything with registrations on the Amazon website itself.
Cheers,
Simon.