I don’t know about after a dog bite, but I’ve had no problem with getting insurance through State Farm with a Rottweiler in my household. All the other major insurers refused. So if you haven’t checked with State Farm, you might do so.
That is a crappy problem to have. Best of luck – it seems like you ought to be able to pay extra for a rider on your policy but I guess they have their actuaries that say it isn’t worth it.