State Farm Leaving Car in Tow Yard During Fee Dispute

Location: Sacramento, CA

My car was rear-ended on 3/27. CHP was called, and CHP also called the tow trucks to take the car (I was not given a choice in towing). The car was towed to the tow company's yard.

On 3/28 I filed the claim with my insurance, State Farm (SF here on out), and verbally released the car to them during that call. SF informed me that I needed to retrieve any belongings from the vehicle by 3/30, as they would take possession of the vehicle on 3/31. Given the extent of the damage, it is already being processed as a total loss.

I went to the yard on 3/30, retrieved my remaining belongings, and signed the car over the SF. At this point, the car is entirely within their ability to retrieve, all actions required on my end have been completed.

I find out on 4/2 via a notice of pending lien mailed to me that SF never retrieved the car. They never told me it wasn't picked up on 3/31, and I did assume they took it given how forceful they were when I filed the claim that it would be taken that day.

In a call with SF on 4/3, they say that the tow company is charging more than what SF's records show as the maximum fees for CHP (tow 215/1st hour, 106/.5 hours after that, max 66/day storage). I went to the tow company, on behalf of SF to request an itemized bill, and their posted rates are what their contracted rates are, which is 468/hr for night time and electric car, and 85/day storage for electric vehicle (night rate for gas vehicle is 319/hr, which seems to be in line for the area, but the tow yard stated fire hazard is why electric is more). The itemized bill SF received is all the itemization done, since it is a flat hourly rate.

SF is now stating that I am responsible for storage fees moving forward, in their boiler plate letter claiming that "We believe a reasonable period of time has passed for you to minimize the storage charges." But they've been fully able to pick up the car since the morning of 3/30, I did do everything correctly to minimize storage fees.

My agent said that I shouldn't be responsible for any of the storage fees, since my required actions were all complete by 3/30 (3 days post-accident). I'm not sure what outdated fee schedule they're using, but even a quick search shows that the rates they listed are not remotely close to the rates in the area.

How do I escalate this properly to get them to pay the tow fees and pick up the car? I'm at my wits end with this, and I'm not sure how to propel them to move forward more quickly. I feel that them fighting about the fees, while not retrieving the car and allowing it to rack up more and more in storage fees, is ridiculous.

I'm not at fault for any of this (the accident, the extended storage), but it seems like they're not remotely operating in good faith at the moment.

Any advice is wholly appreciated, I don't know what to do, and I feel like I'm going to end up paying a bunch of money that I shouldn't have to, and it's just been an extremely distressing situation all around.