Is there a requirement to save the message “off box?” It would easy enough to create an application /IVR style on UCCX that handles all of this on box; both call-in to leave the message, and then for employees to call and retrieve/ listen to it. You could even create a distribution to send the recorded message or notification via email that an updated message is waiting to be heard...
Not sure if this meets your requirements, that’s how I would do this...
-Sean