Sorry to see all of that damage but glad that you're ok.
As for how to deal with the situation? I can't offer any advice but I can say that being honest, forthright, and prompt certainly didn't work for me.
My silver Boxster was totaled 14 months ago (
http://986forum.com/forums/general-discussions/43878-ahhh-my-car-hit-bad-today.html) and I still haven't been able to completely settle my claim with the drivers insurance company!
The insurance company has delayed, denied, and detoured everything in order to drag this out as long as possible in the hope that I would give up. The adjuster even went so far as to claim that I was partially at fault! (the car was legally parked in front of my house and I wasn't even in the car at the time!!). I just keep re-submitting all of the paperwork each time the claim is denied and go another round.
The good thing is that I didn't need their money in order to move on and build my race car and buy the 996 as a daily driver.
I hope that you don't have a similar experience. Best of luck.