had a similar experiance, got paid 2k less than what i thought it was worth, took the payout, asked for first right of refusal on the tender for the wreck, and got the wreck for $1500 parted it out and made about 6k on that, so ended up about about having about 2k more than what i thought i should have got. Yes it was a PITA with having to dismantle the car but somethings are worth it.
Any modified/rare car i have will always have a valuation done on it.
The other option is to forgo claiming on your insurance and claim directly against the other party. The reason that insurance companies often allow for claims when you are on third party insurnace and are hit by someone else is because over all it makes their lives easier than all the people with no clue claiming against the other partys insurance, but that is always an option you have up until you submit a claim with your insurance company.