Since I first posted, I received an email from the Verizon rep and found information on the various devices they'll install. I am hoping it will work out as I describe below (nice and tidy).
The website says the ONT may be installed either outside or inside the house. Since the power outlet for the ONT power supply needs to be inside in my case, I suspect the better location for the ONT is inside my breaker panel closet. There's a single GFI outlet in there already in use by my alarm system, but I can change it to a double if necessary. There is a 18"x12" unused area on the plywood panel, so the ONT could be mounted to it there. There is a phone punch block, a CAT6 cable reserved for just such a situation that goes directly to my equipment shelf, and a junction for the existing coax TV cable.
So assuming they'll be willing to put the ONT inside, this install should be a breeze for them.