Actual cash value (ACV) from your insurance is not the same as an adjusted amount — it's an estimate on their books. I would get another person to look at the vehicle and get another opinion on the adjustment to make sure it was accurate before trying to fight the claims department. If you have any questions, don't hesitate to ask.
I would call up your local DMV or appropriate state department and ask them what to do. Most states allow you to pay a small fee and show an out of state status and they will issue you a temporary paper plate for the vehicle to be relocated.
I'm sorry but your friend's insurance company would not be responsible for your motorcycle since car insurance does not cover the contents of the vehicle, which is what the motorcycle would be considered. If you have comprehensive coverage on the motorcycle, your insurance company will likely cover the claim.