It's an issue with the Magix and DID/PRI integration with hunt groups. With POTS lines, you can assign specific POTS lines to the group and then cover them to voicemail using the time based overflow. With DID, it doesn't work. The only way it is ever going to overflow is the two scenerios you mentioned: (1) Everyone is already on a call or (2) Everyone has logged off.
You could set-up the DID as a user, then put coverage for that user on each of the (4) users. Then, calls to the DID ring on the coverage button of each of the users, if not answered they follow the coverage path for that user you created(which you can create as auto-attendant 1 or whichever in the messaging). Then, instead of log-out (keep it labeled log-out if you'd like) put a DND button on eveyone's phone. Pressing that will essentially take them out of ringing for the coverage button (downside their own extension will not ring either).