It seems from Zen's introductory e-mails that this will not work with their own router. This seems strange because the current set-up works perfectly well, I'm assuming that Zen has got this right.
That seems odd, replicating that setup with the Panasonic DECT base plugged into the FON port on the Fritz!Box should work - it is just an analogue phone connection.
The only potential issue with the phone port on the Fritz!Box is that is does not generate a disconnect signal so call screening devices and answering machines cannot detect when a caller hangs up. If you are not using any answering machine facility in the Panasonic base this isn't an issue.
Alternatively you could deregister the Panasonic handsets from the existing base and register them with the DECT base built in to the Fritz!Box
https://uk.fritz.com/service/knowledge-base/dok/FRIT... You may have to replace the main Panasonic base with a charging only one (like the other handsets use) as some manufacturers phones will automatically register when placed on the main base to charge.