According to the Washington State Office of the Insurance Commissioner there are not specific state laws surrounding this issue so insurance companies have differing policies regarding payment procedures.

Your company may have policy language regarding whether it is necessary to repair your vehicle, or to make the draft payable to a lien holder or a body shop and the owner. If the other party's company is paying they are required to pay either the registered owner or the lien holder, or both.

Most insurance companies will write the check to both the car owner and lien holder when a person still owes on a vehicle since the lien holder still holds the title of the vehicle so has the right to make sure the vehicle is repaired after an accident. The car is the lien holder's asset and thus they have the right to make sure the insurance monies are used to get car repaired properly.

As for the procedures of your lien holder, you can continue to see if they will work with you to get the check signed and handed over to the repair shop. If they will not do so due to their corporate policies then it appears you will have to wait until you are able to save up the money the body shop requires up front to start the work on the vehicle.