For the whole car its going to take some time to find the right buyer. If you're willing to take the time, then that's probably the best option. You must keep in mind that what your car is worth is different from what it will sell for.
I couldn't sell the Rusty Old Datsun complete (although it was a more specialized car then yours) mostly because is scared the two different guys who test drove it at Buttonwillow. I ended up parting it out. That process took six months and a lot of effort on my end to strip, clean, package/crate, and ship the various components. I ended up grossing about 15% more then the full package price but it was a net loss based on the time and effort I put in.
One benefit of parting the car out, you never worry about someone having trouble with it and calling back. And every year the car gets faster and faster as I bore everyone with stories about it