I wish that I’d read this a few years ago. I think that we all have a few voicemails that we wish that we could keep forever, but I lost a few a couple years ago. I think that my current system stores them in a digital messaging system, like you mentioned, so they should be able to be saved. Thanks for the post!
Step 7: If you want to record all the calls you make or receive, select the All numbers option. If you wish to record calls from the numbers that are not saved in your contacts, select the Unsaved numbers option. You can even choose some select numbers manually that you wish to record calls to and from by clicking the Selected numbers option, then tapping Auto record numbers, and then add the numbers that you desire by typing them manually or adding those numbers from your Recents or Contacts lists.

2. Press and hold the number one for approximately two seconds until the phone automatically contacts voicemail.
When you answer calls made to your Google Voice number, tap 4 on the number pad. Participants will hear a robot voice state that recording has begun—this is Google's way of keeping you legal; Alphabet Inc. wants no part of a lawsuit. To stop recording, tap 4 again or hang up. You can hit the 4 key as often as you like to start and stop recording.