Welcome to the forums.
Don't have a Verizon tech come. If you need to pull wires through your walls, you're much better off with an electrician or home-theater installer. They will do a much better job.
You may not need to pull wires. Your FiOS install is setup to deliver internet service to the router over coax. The Ethernet port on the ONT is not active. You can plug the router into any active coax drop in your home and it will connect to the internet. If you have coax drop in your office, simply move the router to that drop and plug in your wired Ethernet device to the router. You should still get good WiFi on the floor below.
Good Luck.