Well... persistance has paid off! When listening to your Google voicemail, you have to hit "7" at the end to mark it as read, which "archives" it. The key to making the VM indicator go off, apparently, was to uncheck the option to send missed calls to the inbox.
After un-checking that option, I called and left a voicemail an the indicator lit up. I then listened through my phone and marked it as read. After hanging up, it took about 30 seconds but the indicator went off. So that's awesome! Thanks to everyone for the info found here!
Also, I found that, strangely, my Obi is recognizing the number calling in -- and I don't have them programmed in the phone, either. It shows on my phone's CID screen, and announces it while ringing. But when I
listen to the voicemail, Google says "from an unknown number". So I found it interesting that the CID is working, and the incoming number shows up online, but Google's
voicemail couldn't seem to announce it.