Do you not have rental car coverage with your insurance?
Chances are, you will not get that information on your own.
Reason: Privacy Act.
No one will volutarily give you that information!
Exactly... They will not release that information unless you are an attorney... But that is where you're insurance company comes in! They can get that information in a matter of days.
Any attorney will take that case. However, for one to do so, you'll have to pay them up front and then when the other party is found liable, you can recover attorneys costs from them. Good luck getting that though!
The shortcut to that, is to go through your insurance... But you seem to want to do it on your own.
Point is, and while you're on your own, you're going to be spinning your wheels, and the only thing you're gonna get, is frustrated!