You need to do it the old fashioned and most dependable way. Forget the Carfax, which is right only part of the time. Take the vehicle to a dealer and pay them to do a thorough inspection and diagnosis including putting the car on the lift and looking for previous damage. A dependable dealer will give you a much better idea of condition and where you are starting from than any anonymous public records search.
I wouldn't worry too much about the spotty information from the first owner on the Carfax. I'm curious about the second owner though. Is the second owner the Danbury dealership that is now selling the car? It seems like it based on the miles. I haven't done much with Carfax but I didn't know a dealer would show up as an owner on the Carfax for a trade-in. Is that the way it normally works?