I am not understanding your question or questions.
You just have coax cable running. Okay. Are you trying to extend the connections to the places other than where you put the router?
Are you subscribed to FiOS TV service?
Have a Verizon technician came to install the ONT yet?
If you are looking for a router with coax MoCA port, I would suggest buying G1100 from Amazon or Ebay. Used equipment are fine, I rarely see malfunctioning network devices. You may want to consider saving some money.
If you do not have Verizon DVR, your can keep your router at its place and buy MoCA adapters for the STBs.