Aaron --
Many people are cleared to fly a few weeks after surgery. I know this because I know people who did it. The problem is that they all caught various types of illnesses. Flying is a great way to get sick! Personally, being almost four weeks out of surgery, the thought of a road trip is way more appealing than flying. Flying sounds awful! I don't blame you for wanting to drive back home instead of flying.
I am assuming that you have a leisurely road trip back in mind. You definitely need a driver! You need to totally trust everyone that it would be highly unlikely that you will be successful driving all by yourself, even if you are able to drive for short periods. Renting a comfortable, cushy van or RV would probably be the best option, although maybe you would be more comfortable in a regular car with egonomically-correct sports seats.
This is something you won't know until a few weeks after your surgery.
You will need to carefully plan a route back with very regular stops to get out and walk around as well as hotel stops that let you get plenty of rest. One problem that you will have is sleeping; as you know from reading this forum, most people sleep in recliners or adjustable beds after surgery. High wedge pillows are a possibility, although I don't know if others have really liked them; they weren't good for me.
Also, very importantly, your route will have to stay to the interstate and high-populated areas as much as possible so that you can quickly get to a good hospital in case of emergency. This will not be a time to get your kicks on Route 66.
I wonder if the websites of popular "destination hospitals" have more info about traveling back home after surgery. Examples of the Mayo Clinic and the Cleveland Clinic (specificially for hearts) and other hospitals that have people travel for other reasons, like Henry Ford Hospital in Detroit. Maybe I'll ask my Dad on your behalf; he is a doctor at Henry Ford, and they have people come in from all over the world for various types of transplants.