Is my insurance companys offer or behavior reasonable?

My wife was involved in an accident. She entered an intersection just as the light had turned orange. A car took a left turn into her. It was raining. My wife called 911. A cop came. Talked to the other party. Came to my wife, asked her if she had someone who could pick her up. Yes. But she protested that he (the cop) had not taken her statement. Very well, tell me, he said. My wife told him her side of the story. The other driver was standing close by. That person insisted that my wife ran a red light. My wife said no. The cop said he had taken down both sides of the story. The other driver left. The cop offered to drive my wife to a nearby mall where she would wait for me. En route he told her that he didn't wanna say it in front of the other driver because he didn't wanna rile that person up, but, the cop said, it was that other driver's fault. Even if the light had turned red the other driver was obliged to make sure the intersection was clear before taking the left turn. That was that. We called our insurance company. They asked us if we wanted to file through them or pursue the other party ourselves. We didn't think we had the capacity to pursue this thing ourselves. So we went with our insurance company. A day later that other driver directly (that is, not through his insurance company) approached our insurance company and filed a claim. My insurance agent asked him to work through his insurance company. Meanwhile the car had been taken to a body shop that our insurance company works with. We have a 99 Acura 3.0 CL. With only 75,000 miles and in excellent condition. The body shop came back after a couple of days and said just the cost of fixing the body and the front suspension that had taken a hit was about $5300. The car had been hit on the side with the front tire area/driver side door the main impact zone. But the damage had also knocked out the front bumper. They had not disassembled the car because they figured the cost already implied that the car was totaled. Our insurance agent confirmed that. Today she called with an offer: $7200. Our $500 deductible would be subtracted from that and refunded to the extent my insurance company is able to recoup the cost from the other company. I checked the blue book value. The retail value came out to be $6300. I am disappointed because my car was in excellent condition, very few miles. Plus, for those who recall the 3.0 CL line, the styling is unique. Acura doesn't make this car anymore. We planned to keep this car for another five years at least. Our insurance agent really wanted to wrap this thing today. I had a difficult time getting like a couple of days extension. They will continue resolving this through the other insurance company. What I am grappling with is this:

1. Based on my (long!) description of events, are the chances good that my insurance company will be able to recoup cost from the other party.

2. Is my insurance company offering me a fair price? Nada.com $7625. Kbb.com $6300. Autotrader has listings that average $6780 for cars with an average of 102,000 miles. My insurance company is offering $7200 for a car with 72K miles. (They are also offering an additional $500 as compensation for title/other fees, but I figure that is separate from the actual cost.) Should I be doing something else to research my car cost?

3. My insurance company wants me to sign off on the offer so they can give my car up to salvage. Is it okay if I take whatever time is required for due diligence? Also, can I release my car to salvage and still maintain negotiating leverage?

4. If I play hardball over an extra $500, will that embitter my insurance company and incline them to punishing me more in terms of how they negotiate with the other driver's insurance company, or in terms of jacking up my insurance rates?

Any help will be greatly appreciated.

Thanks.