I've not tested this deployment, but others have reported doing this. It should work fine. They key point is to have no other MoCA devices on the coax, just the one at the ONT and the one at the router. To avoid the possibility of this even happening, I recommend using a point-to-point coax link if your cabling supports this.
Note that this is not supported by Verizon. Not a big deal, but you won't be able to ask them for help. Instead, come back here.
Same thing if you switch to a non-Verizon router (by the way, it's a router, not a modem). Verizon support will end at the ONT if you don't use their router. Since FiOS is very reliable, you understand the technology, and found this forum, you're in good shape.
If you want a Verizon supported option, put the router near the ONT. Connect it to Ethernet for WAN and coax for MoCA LAN. Then buy/rent a Verizon extender and put it in the office. You'll have both WiFi and Ethernet ports in the office. You can have more than one MoCA device on the coax. Note that if you have the G1100 router, the speed will be limited to under 500Mbps.
To switch to Ethernet WAN, I suggest you contact Verizon support via chat. Sometimes the phone reps don't understand the request. It takes just a few minutes and doesn't cost anything.
Bonus: Once you get the ONT switched to Ethernet WAN, you should be able to order 1Gbps service without an upgrade fee!