That's BS!!
I'd raise Cain and make them to come to you.
They need to get off their butts and do their job. After all, isn't service part of what you are paying for in those big ol' premiums?
You don't want your car sitting in a tow lot somewhere, waiting for them to get around to looking at it "when they have time".
You don't owe them a G Darn thing.
This is a disaster and they have disaster teams that get paid extra to work situations like this.
You, on the other hand, are the victim of this disaster and first and foremost, their customer, admittedly one of many, but still a customer....... And the customer comes first, right?