If you can, stick to using Ethernet WAN from your ONT to the router. You're going to be better off with such a setup when it comes down to latency. Since your friend has Ethernet WAN and a Coaxial connection present, he has to use Ethernet for his connectivity back to the ONT, as Coaxial will max at 100Mbps. It's there strictly for the Set Top Boxes. If you do wish to stick with Coaxial, the rule is, the less splitters in the mix, the better. If you can eliminate everything to just one splitter that is also compatible with MoCa, that should give you the best possible setup. Each splitter attenuates the signal.
By any chance, are you able to get the model of the ONT Verizon installed? A picture will do if you're able to take one. This is the big box that connects up to the Fiber. I'm curious if you're in a BPON area. Otherwise, I really believe someone should be sent out at this point if it's not the connection to/from the router. You could have dirty fiber which can cause issues for others.