The Resolution!
The supervisor himself came out yesterday morning with one of his techs, strapped the dish to a meter and walked all over the property - including the roof - to see where he could get a signal. They wound up mounting the dish to a large pine tree in my back yard, running the cables overhead to the house, and strapping everything down. They even grounded the multiswitch!
Oh, and it took them less than 2 hours to do the whole thing.
I asked the guy why his installers didn't seem to know what they were doing and he didn't have an answer.
Yeah, I know the tree mount isn't ideal - but as long as it gets through the winter I don't care. When spring comes I'm re-mounting it on a solid post myself. Now that the infrastructure is in place, I can do that much more easily. Oh, and the DirecTV CSR gave me 6 months of free HD service for my trouble - on top of all the other stuff they had already given us for not canceling our service and switching to FIOS...
I do plan to e-mail that DirecTV rep you guys mentioned and let her know the situation. It remains amazing to me that a company that prides itself on customer service can let installers like this come to people's homes. After all, that's the only face-to-face contact you'll ever have with DirecTV - and that's a really bad image to be sending to your customers.