I didn't have a choice
Yes, you did.
There's always a choice. There's a choice when a gun is put to your head and the hammer cocked. The choice is to obey or die. Granted, not a very good choice, but still a choice. So, never defend your mistakes by saying you didn't have a choice. That's just a cop-out.
And besides, if I gave the keys of MY car to a friend who then disappeared with it, that would be considered theft, right? So, I don't see how it's really different with a rental car.
I agree. Conversion is a form of theft that's defined in the criminal statutes. Your insurance company was right to pay for the car.
the rental car company is trying to charge me $5000 for the time between the rental and the filing of the police report.
So they can just charge me whatever they feel like? I mean even a month at $50 a day is only $1500... I just can't rationalize how that is ok...
Would it do any good to write the company? Or try to speak to someone who might care about how their company is viewed?
Yes, they can charge you whatever they want. The better question is: can they make it stick.
You have a few choices here.
You can ignore it and wait till the rental company sues you. Then they will have to justify it in court. Unfortunately, they probably won't bother spending money on a lawsuit, they'll just send it to collections and trash your credit. That way they don't have to prove anything.
You can try to negotiate a cash settlement at the daily or weekly rate. But I suggest you do that higher in the food chain, like with a corporate executive. Make sure everything is in writing. Make sure you have the cash to pay what you offer or they aren't going to take you seriously. And know that nobody at the company will care how the company is viewed in this matter. It's all a matter of money. There's no question that you owe something.
Another alternative is that you hire a lawyer to defend you from the rental company's demand. That includes the possibility of you filing a lawsuit for a declaratory judgment that you don't owe the money. Count on paying your lawyer many thousands, not getting back any of his fees and still having to pay something to the rental car company.
Bottom line, acknowledge that your mistake is going to cost you money. Then see about getting it down to a reasonable amount.