Here is my advise, having dealt with a totaled car in the past here is what I'd reccomend.
First, call the office of the insurance commissioner for your state, explain what happened and ask what process the other drivers insurance co should follow. Tell them you don't know how this type of thing works, they will tell you the basics...
Second. let the other insurance company know that you have spoke to the office of the insurance commissioner, sets a playing field for them not to jack you around.
Third. search for cars like yours. same year if possibe, same options etc... and see what they are selling for. Get newspapgers, ebay sales info, look for similar cars for sale on this site, NADA and KElly Blue Book numbers. Collect all modification papers with prices etc... You need to establish what your car is worth on the open market today... Talk to car dealers and see that they would sell the car for if it weren't wrecked
Fourth, establish what all the extra work you now have to do is worth. Collecting all this info, finding a new car, all the time you put in. Yes the "love" you have for your car is worth money, it's sentimental value to you. Use what you make at work as an hourly rate benchmark for all the time you spend, even time talking to the insurance company on the phone. Also document all driving time and miles you spend doing all this work, they need to pay that too...
Fifth, they should be providing you a rental, no questions asked.
Sixth. make sure you don't have any injuries, back neck etc... if you feel anything "not normal" get looked at. In TX the typical settlement amount is 3x medial bills if you have any injuries that require treatment.
Seventh, never settle quickly... make them wait, don't accept the first or second offer. Get every damn dime you are owed. If you find a Tbird replacment and it's 600 miles away, make them pay to have it delivered.
Eighth, if you don't know of feel uncomfortable about anything the ask or tell you consult your insurance agen, an attourney or email me. Don't do anything until you are 100% satisfied with all the arrangements etc... You own this process, the timeline and how it al happens, they answer to you!!!
Let me know how it goes, you can PM me...
Patrick L Beauchene
Austin TX