The first model I tried was the KX-TGB210. I don't see it listed anywhere as compatible, although the specs suggest it should be: still, as a weekend special at Harvey Norman for $9, it was worth a crack. Based on comments in another GeekZone thread (id=110628) I then bought a KX-TG1611NZ on TradeMe but, even after deregistering it from the base station, it won't register with the Fritz!Box.
Here are the settings on the Fritz!Box's DECT page:

I've toggled with the Troubleshooting option too, but that doesn't appear to affect the outcome.
If anyone can suggest further steps to try, I'm keen to hear. Thanks.