I wouldn't try too hard to be legal. Just bust a move to your home state and ask for forgiveness if you get pulled over anywhere along the way.
In my personal experience, I purchased a car in Maryland and drove it home to Washington State. Maryland required the seller to turn the plates into the DMV so I had nothing to work with. I looked into what the states I would travel through required for temporary transportation of a vehicle on public roads and it varied greatly. Some required a simple fee and trip permit, others required state inspection by the state police and everything in between.
In the end, I put a piece of cardboard in a license plate frame in the back with "In transit to WA State" written on it. Pulled over once in Ohio for being a hoon driving 90mph. All they really wanted was for me to prove the car was mine and to get the hell out of their state.
By the way, this was a SCCA Showroom Stock B racecar with meatballs, numbers and sponsors all over the damn thing. (See below-not exact to when I drove across country) Stuck out like middle aged man at Taylor Swift concert. And only that one time in Ohio did I experience any issues.
Like I said, jump in, drive it and ask for forgiveness. Just my 2 cents.
