I've had good negotiating result getting the 1st offer from the first dealer then call the leasing manager at the other dealers to get their price. Use the same features and model to get prices.(Note: the leasing and internet sales manager normally make a deal and has the authority of a real manager so you don't have to dicker with some sales puke who can't do squat without going to a manager.)
Also the last two days of the month the managers try to make quota (commission/bonus time) and will cut some corners to get a sale when they are close to the bonus.
Where you get the shaft is trade-in. In your case, you have insurance money and so can do a partial cash deal. (All cash gets you the best price on a new car.)
Always check your credit union, bank and insurance company for their rates on a new car, they usually beat the dealer yearly %.
Dealers make most of their money paying below market for trades (remember you are getting "traded" not them.) The dealer then shines it up and sells it at big markup.
The best producing salesmen are in used cars as that is where the big commissions are. All in all if you have a used car sell it yourself, get cash then you are in the best position to make the car "deal".
The salesmen call the trade in evaluation, (amoungst themselves) the "devaluation" to pay a smaller amount for your car.
Also the "dealer" will high pressure you to buy a car off the lot, even if it is not the color or features you wanted. The dealer can and will find your car at another dealer for you and trade one of his cars for the other dealer car if you tell him to or no deal.
Edited to add: You will be sent to the "finance guy or gal" at after you make your deal. The dealers make a ton of money on the stuff the finance person tries to sell you. Just say NO and save some money!!
Some dealers also put all their trucks in a spray-in bed liner, for example, and add it on to your sale. You don't have to take it. Just go to a different dealer or tell them you are not paying for it.
I hope this helps!!