My wife and I and two kids under 5 drove Massachusetts (coast) to Cody, Wyoming (over 2,300 miles) in under 48 hours in Ford Escort wagon. (we were in our 30's then)
We stopped for a swim at one place and caught 3 hours sleep in the Dakotas, but did stop in restaurants for the most part to eat. Th e kids did great.

It was a bit grueling at times and we did not plan to do it this way, but it worked out.
It's essential that both of you are capable of sleeping while the car is in motion. I can , my wife can't very well. That way your replacement is ready to take over when you need them to.

I agree with skipping the caffeine (and sugar), at least until the end. Carbonated water I drank in droves on my long drives.
Switch drivers more often towards the end. Books on tape can be great for some.
I find the morning hours when the sun starts to rise the danger time. It's like the body says "Whoa, I need to go to bed".
You have only one sunrise, so don't sweat it.
Your timing is pretty good, but I would try and time it so you are there before the sun goes down on the 2nd day.
Don't be afraid to take a sleep break if it gets too much.

Happy trails,
John