This can work, but you do need to be mindful of the difference between MocA LAN and MoCA WAN, of which the G3100 supports both. The frequency used for MoCA WAN is the 975 MHz - 1025Mhz range, and is typically used in a FiOS Setup only between the ONT and the router. For MoCA LAN, this is used between the FiOS router, any Coax connected network extenders, and any Set top Boxes. This operates at 1125 MHz - 1425 MHz.
If your MoCA adapter can operate at the MoCA WAN frequency used by the router (it is best to have something which can be manually switched, using a slider or DIP Switches), you should be able to use only one adapter, stationed where the ONT is. You'll need to use Band C4 specifically Otherwise, if you need to use the two adapter method because your adapter only works in the LAN frequencies (as most if not all that I've seen do), dedicate a single piece of coax between the "ONT side" and the "Router side" MoCA Adapter, where no points touch other Coax splitters or cables in your home, so you don't end up creating a Layer 2 Bridge and sending your Internet connection to something other than the router. It happens and you'll have a bad time getting things to work.
Verizon normally doesn't support using MoCA for speeds over 100Mbps, even with the MoCA 2.0/2.5 method some people use, mostly because older MoCA Technologies in the ONTS and legacy routers, despite claiming 200Mbps throughput (as an example), only have that as the "total aggregate" rating. Meaning if you have a 200Mbps symmetrical Fiber connection but you try to hit both directions at 200Mbps each, MoCA will limit you to 100Mbps in both directions, or 200Mbps in one direction otherwise. This also becomes a handicap if you choose to get Gigabit someday.
It would be best to run some CAT5e if you want to move the router, even if it ends up following the existing Coax run so that Verizon can support this in the future without too much hassle for you, or another homeowner/family member. If it has to go outdoors, make sure Outdoor rated (preferably Gel filled and with a shield tied to a ground) cable with a solid copper core is used. Once the virus scare is sorted, a Handyman, Security System Installers, or Electrician can help with this, as can Verizon.
Another alternative - Verizon's network extenders that compliment the G3100 can uplink via Coax without any fuss, and they have a Gigabit Ethernet switch inside of them. Your router can remain where it is, and all you have to do is add a splitter (or connect an unused piece of coax) to your existing Coax network, and both Wi-Fi and Ethernet are extended through the Coax cabling. The device is here: https://www.verizon.com/home/accessories/fios-home-wifi-extender/
Hope this helps.