My only experience with Geico was nearly twenty-five years ago when my then soon-to-be Mother-In-Law backed into my brand new truck, broadside. They were wonderful with me, settling the claim generously and expediently. That was not so much the case with her; they fixed her car and then canceled her insurance although she'd had no prior claims. Laws vary from state to state but here you would have the upper hand, being the victim of someone else's poor driving. Tell them you want your car repaired, period. It is a collectible and you do not want a salvage title, so you shouldn't have to take that route.
Don't sign off on anything that is less than 100% satisfying to you. Good luck!
Dwayne