EDIT:Ignore this post and read farther down.
I assume from your question that right now the ONT fiber gateway interfaces with the G1100 by Ethernet not by Coax. This is what you would do.
1. Log into the G1100 and go to the "Broadband" connection and see if it lets you release your IP address. I don't remember if this is possible or effective.
2. Disconnect the G1100 from the ONT and plug the ONT Ethernet into the uplink port for the google wifi. This will become your primary router. You may need to call Verizon to have them release your IP address and make this your regular IP.
3. Once your Internet is up and running with the Verizon router.
4. Plug a laptop into the G1100 via Ethernet. Log into the admin screen and do the following
a. Disable the broadband/Internet connection.
b. Go to the administration for the LAN (I think it'll be called "Home/Ethernet" or somesuch) and (1) disable DHCP and (2) give it an IP address in the subnet of your google wifi network which isn't in use (e.g. if network is 192.168.1.XXX, give it 192.168.1.255) Note, once this happens, your laptop will stop being able to talk to it through the Ethernet since it won't be at the same IP address and won't be doing DHCP for the laptop.
5. Plug an Ethernet cable into one of the local networking (not uplink) ports of the G1100 and the other end into a LAN port of your google network router. If unplugged, plug a coax cable back into the MoCA LAN port of your G1100.
The G1100 should now act as a MoCA bridge, bridging the Tivos via MoCA to your local network.