Not across the country, but I have done 600 miles in a single day with my tank.
If you are able to, and I understand if you can't due to the distance, it may be worthwhile to try and move just the tank by itself without stopping but for short breaks and such once you get it loaded. I've also heard of folks having their corals and livestock shipped to the new residence and draining the entire tank and boxing everything not alive up.
I put all of my corals and rocks in a cooler and traveled with them in the cab of my truck. My fish I put in a black trash bag lined foam cooler with a temperature monitor and a battery operated air pump. I drained my tank to the point where there was just enough water to keep the sand wet and boxed up all of my equipment after cleaning it and drying it off.