So this has taken some time for me to figure out, I had some questions after switching from Android. It seems I was not alone with the issue of using Google Voice/Hangouts for voicemail on iPhone. This will reduce the number of rings when forwarding to your Google number.
So I think the first thing is to follow Ting's instructions for Call Forwarding, https://help.ting.com/hc/en-us/articles/205421988-Call-Forwarding
I use the first three Call Forwarding codes, *61..., *62..., and *67... codes.
The next step is go to www.google.com/voice Settings > Calls > Check- Enable Do Not Disturb
One caveat however is if people call you on your Google number, it will go straight to voicemail. So this works best if you are not giving out your Google number, and just using Google Voice/Hangouts for voicemail.
I also have under the Calls Settings, Send Missed Calls To My Email, checked. So if people do use your Google number to reach you and don't leave a message, you can see who called. From what I read, the Hangouts team is maybe working on a better missed call option in hangouts.
In addition I am not sure if it matters in setup, but I DO NOT have my Ting phone number attached as a phone number under the Phones settings on the Google Voice site. It just lists my Google number, and the option to forward calls to Google Chat, which I leave unchecked.
One more thing I do... Disable Ting Voicemail in device settings.
Hope this helps!