Update #3
Seems like getting my Insurance Company involved sped things up a bit. Geico determined through retail listings, that a well equipped Hybrid XLE, like my car is, worth a little above $16,000 in my area, Seattle and Spokane WA Metro regions. With this information, Geico agreed to authorize the repairs of my vehicle. Originally, they claimed the vehicle was worth less than $13000. All of the Toyota Manufactured Parts arrived today and the bodyshop is getting them prepped for paint. There is no frame damage to the vehicle, but along with all of body repairs, additional items made the repair bill go above $9000. After the body shop is finished their repairs, they are sending the repaired vehicle to my local Toyota Dealership for a four wheel thrust alignment and a hybrid system diagnostic check. Any hybrid defects will be repaired at Geico's expense. The bodyshop says the car will be done in two weeks, pending the dealers workload. Geico still is complaining about minor items with the bodyshop like why both headlight assemblies need to be replaced. Also, the right shockstrut assembly is completely unusable due to damage. It seems, the replacement parts from Toyota are upgraded in many ways over the components originally installed in 2012, thus making the left hand shock strut installation incompatible. Toyota says the undamaged left hand shockstrut assembly needs to be completely replaced with a new strut assembly. The Geico Adjuster is arguing on why only certain parts can't be replaced rather than the whole assembly on the left hand side. With everything in the final stretch, I visited my local Toyota Dealer and cancelled the Rav4 preorder. They cheerfully returned my deposit cheque and mentioned that I should keep them in mind if I change my mind and decide to trade in the Camry.
Finally, the bodyshop has been taking extensive photographs of the vehicle damage before and during the repairs. They are going to give me a digital and paper record of the damage, itemized repair bill and warranty for their work and separate documentation from the Toyota Dealer. Hopefully having such documentation will keep my vehicle's value from plummeting due to the major accident.