Well, color me embarrassed. The whole fiasco was user error.
I was 100% certain that Verizon only brought a coax cable into the house. And, interestingly, a VZ tech who came to the house a few days ago when a new set top box wouldn't install thought the same thing when he looked at my setup. But I just noticed that the "printer" cable had a lot of loops sitting on the floor behind the cabinet where the router and printer are located and I thought "I don't have a printer cable that long." I followed it around and discovered it goes up and out the same way as the Coax. My "printer cable" connects to the ONT! When I was hooking up the TP-Link initially I must have pulled it thinking it was the printer and then plugged the TP-Link into the WAN port. What is even more confusing is that worked. So the TP-Link must have somehow been able to get an Internet connection from the FIOS router through the MoCA WAN bridge and back to the ONT via coax. And it somehow fed that service over to the FIOS box which NATed it to the internal LAN to serve the set top boxes. But, when the TP-Link was not in the WAN port the FIOS router was unable to get an Internet connection thru the coax by itself. Strange. If I hadn't experimented with the "printer" cable I might never have sorted this out.
Thanks for all the help and don't trust me on anything like this in the future.