Handling Robo Calls through the system

I'm curious to see if the community has any feedback on this:
We've had complaints about users not being able to get past the menu. We've entered tickets to Zoom but their data shows that the users never presseda menu option. However, the users claim that they did. 

In an effort to lose those users, we updated the call flow to make sure the call goes to  voicemail for the team to monitor. 
Doing this has inundated us with voicemails with dead air. There's roughly 60+ voicemails on a given day.

What can we do to better handle this and avoid the unneeded extra noise?