Thanks guys for the tips already. Some additional color:
This car will likely be a challenge to sell privately, as it is a two door and I have done some research/leg work on the current market. There are 30 of the same make/model for sale at dealerships across the country, with an average time listed on the market of 47 days. All the cars listed over 30 days have dropped their price at least 3,000, which would be close to what Carvana was offering.
I don't want to make two car payments at the same time. One camry I like fits in my *new* budget and I can potentially throw commission checks over and pay that loan off by Christmas if I am aggressive. That said, Paying and insuring two cars is not something I have any interest in.
The total monthly cost (payment, average gas, insurance) for the car I want to unload runs close to $800/mo. The car I would be buying all in cost is easily half that, if not less. We are talking 20 mpg to 38 mpg and insurance difference of 28%.