Totaled truck... advice on moving forward with insurance.

Guess I could use some assistance with figuring out what to do in this scenario.

I undfortunately was involved in an accident and totaled both my tractor and trailer.
This accident happened March 26th and I just now received the paperwork to sign. So of course it has been sitting at the towing company for the past month. The initial bill was $6500, but after the storage Im sure its going to be over $10,000. I'm waiting for an up todate bill tomorrow.

Speaking with the insurance adjuster today, he explained I had $5000 for the tractor and $5,000 for the trailer. He knows that the towing/storage bill will exceed this figure and said often times people will negotiate and agree to give the towing yard the damaged equipment in exchange for the remainder due to them.

The insurance adjuster took his time of course with getting a quote and upon his admission, he spent a week calling the wrong appraiser, due to a wrong number. So that Is over a week of time that was wasted that incurred more expenses on this bill.

In this situation the truck payoff is around $45k, which I had coverage up to the amount. There is a $5,000 tow charge limit, a salvage buy price of $6,000 and a $1,000 deductible. netting = 43,000 net.

The trailer was a rental and has a the cash value is about $6,000 less than what I had it insured at. They told me in the insurance contract it states, they will pay the lesser of the 2.
So, I've got a cash value of $18,500, $5000 tow charge limit, Salvage price of $2,010, and a $1000 deductible = $20,490 net.

This is my first major accident and this is new to me especially regarding the tow/yard. Any advice or suggestions with moving forward would be greatly appreciated.

The truck is a 2014 KW T680 Paccar engine with around 540,000 miles. If it was closer to me Id part it out and think Id be able to come out better than not. In negotiating with the tow yard will this give me some leverage?

Here are some pics:

The truck didn't completely turn over it was more sliding than anything. I imagine the engine and transmission still have life and minimal damage.

 

I carried the insurance for the trailer.