Their investigations can take up to a month. If you are without a vehicle, get a rental car and put in a claim for reimbursement for that. Or, ask them to pay for your rental car up front, a lot of insurance companies have deals with rental car places.
Secondly, there's nothing you can do to get them to pay KBB value. That's not a publication used by the auto industry. Something closer to NADA is what you're going to get.