Not sure what you're trying to fight for here. The value of your car is probably around $5000, insurance companies will generally write off a car when repair estimates come close to 70% of the replacement value, so say $3500.
Sure you can scavenge the internet and junkyards for parts and do the repair in your garage for $1k, but your insurance company isn't going to do that.
I don't see anything terribly egregious in the estimate, they're basically covering their bases. The last thing an insurance company wants to do is go low on the estimate and then find that the car needs more work and they should have written it off in the first place. Remember that if the insurance company agrees to fix the vehicle, they then are responsible for fixing it to the same or better condition that it was prior to the accident. For a car this cheap, with that much damage, it's just not worth the headache.
When I wrote off a van some time back the insurance company gave me two options.
1) Take the write off amount and go shopping..IIRC $10K
2) Take the wrecked van and the payout minus what they would get for the wreck IIRC The van and $6-7K
Since the van had been used to remove a fire hydrant I went with #1. Also the van was lien free favouring #1.
The OP has a different situation in that he owes on the car and the first cheque goes to the finance company. I'm not in the market so feel free to correct numbers.
Redger says a value of $5K so Insurer cuts a cheque for say $2k to the finance company and $3k to the OP and reclaims a bit from the wreckers, say $500. OP goes shopping with $3K in his pocket
Alternate #2 OP keeps the car and takes $4500 in hopes of doing it himself but keep in mind that $2K of the money belongs to the finance company and they might want it now because the wreck has no collateral value. OP has a wreck and $2500. I'm not sure who picks up the tab for storage and disassembly. It won't be free.
Where is the car now?
If it isn't at the OP's home it will need a tow or reassembly. A tow could be a couple of hundred but reassembly just isn't going to happen due to costs and liabilities.
If the OP needs a car for work and has to rent, the coin in his pocket will be gone before the car is fixed.
The curse of the scenario is that the OP may have been very comfortable with the car from a reliability viewpoint. If you go shopping with $5K you could be buying someone else's troubles. If the difference between the options was closer the repair could be somewhat justified.
There are no good choices just less bad. I can't see how fixing the car would make sense.
Feel free to adjust my numbers.