The only way you are going to solve the issue imo, is to get someone from Zen [an engineer perhaps] to visit you and then let him/her test with and without the DVR connected.
But it is unlikely that video devices connected by Ethernet could be the cause.
A crossed line could, but Zen have already ruled that out.?
There is one possible reason though, the DVR might have developed an internal fault that is messing with other external wiring and somehow making calls from your line, if as you say the problem goes away when you disconnect the DVR then it is part of the mix somewhere.?
Edited by deleted (Thu 12-May-16 01:10:48)