Do not accept any legal advice other than from a lawyer licensed to practice in your state.
That said, good grief.
The insurance carrier for the opposing party, Geico, has no contractual duty to you, unless Texas law changes that. Your girlfriend the attorney should be able to answer that for you. They do have a contractual duty to their insured, which, generally, is to pay whatever damages their insured is adjudged to be, or could be adjudged to be, liable for in a court of law, and which fall within the contractual terms of their policy WITH HER, unless Texas law changes that.
If the contractual duty of your insurance carrier to you is better than that deal, act accordingly.
It sounds like Geico is trying to hit with you comparative fault. I have no idea whether or not Texas has that in its law. My state also has a doctrine called "last clear chance" which is pretty much what it sounds like. I have no idea whether or not Texas has that in its law. Your girlfriend the attorney should be able to answer these things for you, and their applicability, if any, to the facts of your accident.
My suggestion from a state away would be to make a determination of what your provable damages are under Texas law, and then demand more than that from the insurance carrier so you have room to negotiate. In my state, the measure of damages to personal property is the difference in the value of the property immediately before the occurrence, and immediately after. Sometimes the cost of repair can be considered as evidence of this. In some circumstances, there are some other incidental damages that may be available. Your girlfriend the attorney should be able to answer these things for you.
At one point in time, I owned a couple of auto auctions. Cars are a commodity item. They are all average condition. That's not to say you cannot get more than the average if you have proof to cause a deviation from the norm, and are willing to let them buy the car, but the starting point ( and probably ending point with garbage like GEICO ) is probably average. Or worse.
Telling the insurance agent you are going to do bad things to them and their insured is laughable and a poor negotiating tactic, imo. They don't care. They were threatened by bigger and badder people than you before you ever called them. They didn't care about that, either.
Hate to see this happen to a nice car, but such is life. Since it looks like your carrier is out of the picture, I might well demand the cost of repairing the car to the condition it was in before the occurrence if that is an available remedy under your law, but that's just me. Your girlfriend the attorney, who presumably is licensed to practice in TX ( I am not ) should be able to answer these things for you. This is not rocket science stuff. Do not accept any legal advice other than from a lawyer licensed to practice in your state.
Good luck.