Outgoing VM Message Garbled or Cut Off at the Beginning

I have a rather strange problem with my cox voicemail. Intermittently, my greeting is garbled or cut off at the beginning of the script. This happens whether I record a personal greeting or use the default with only first and last name. I have replaced the modem (PW6), checked and re-checked the connections, and rebooted and reset the modem multiple times, all to no avail. I can make and receive calls with no problem, but when I or anyone else calls the number and waits for the voicemail to pick up, the problem occurs about half the time. I have voicemail set to pick up after 4 rings, and have noticed that sometimes one or more of the rings are shorter or longer than usual. I have tried setting voicemail pickup for fewer or more rings, but the problem persists independently of that setting.

Does anyone have a clue what could be going on? I have talked to support, and they have suggested it could be a line issue and I might need to have a tech come out.  Just thought I would check in here before to see if anyone else has ever had this problem before I go any further. Thanks