Insurance companies - can i reduce the agreed value so they write off my car?

[SE Ute]

Just got what i hope is a simple question for anyone that knows a bit about how insurance companies work.

I've got $11,000 worth of damage to my ute, it's pretty nasty, got t-boned in the drivers door, and she's gone a bit banana shaped, not driving straight etc etc, so i don't really want her back, i really want her to be a write off. If it is fixed then i'll probably move her on ASAP when i get her back. I don't think it'll ever be the same.

Anyway the problem i've got is it's insured for $17,550 agreed value, so they won't write her off, they want to fix it, apparently damage needs to be greater than 70% of the value of the vehicle for it to be a write off. The thing is though, i'd be happier with an amount less than the agreed value. I got her valued a couple of weeks back as a trade in on a new car, and the dealer was only going to give me $8,500. I reckon i could probably get $12,000 to $14,000 tops if i sold it privately, and i'd be happy to take $14,000 from the insurer, if they would write her off. Save me the hassle of selling it privately etc etc...

I've asked the insurer if we could agree on a lesser value for the car so it is a write off, and i think i must be the first person to ever ask them, because the first person i spoke to didn't understand and the second person is going to get someone else to call me back.

So, i'm hoping someone on here might have done a similar thing, or know a bit about how insurance companies work, and can tell me if they are likely to agree to what i'm proposing to them, just so i can push them the way i want with a bit of confidence and won't get told a furphy so they get what they want..

Thanks guys. Sorry about the long post..