I have my own WiFi router and I do not want the free VZ-supplied wireless. I would also prefer not to use a VZ-supplied router, either. Does anyone know how much of a hassle, if any, I'm going to encounter when I make this clear to the installer?
Are you getting FiOS TV? If so, you need the Verizon router as it acts as a bridge to the Coax network so the STB's can get their guide data, etc.
Let the installer do a proper installation with the FiOS router and then turn off the wireless in the router configuration if you don't want it. Install your device behind the Verizon router in "access point" mode or in WAN-to-LAN mode and place your router's address in the Verizon router's "DMZ".
If you're not getting FiOS TV, then simply ask the installer to provision you via ethernet (you'll need ethernet running from where the ONT will be installed to wherever your router will live) and let them install the Verizon router. Once complete, you can replace the Verizon router with your own router after the installer leaves.