Most important part of following the Interstate is the opportunity to land on it when the unexpected occurs.
Second, they usually follow the lowest route possible. Study the charts for power lines across from one ridge or mountain to the other, and if you unexpectedly meet a big one, go under, not over. They are much more than 20 feet above the road, and you can dive better than climb in the mountains. Small power lines are the opposite, they are low, and going over requires little climb.
Remember to keep right when following roads, you are going to meet more planes than you might expect, and they are hard to see against mountain sides. If each one is flying at about 100 mph, the closing speed is 200, which is less than 20 seconds per mile closure rate. 20 seconds is just a long scan, or grabbing a drink from the water bottle.
The thread on the "Scenic emergency landing" is a perfect example. I have known several people who landed on roads and highways, and all have gone well. Plus, there will be someone to give you assistance if you need it.
All of them flew their plane again, one, the same day an hour later. All three had different reasons to land.
Others have said you should get the longest days done in the eastern portion of the trip, and I agree. Your endurance will be at its best there, and the weather the most co operative. Dawn to dark is acceptable there.
In the high country, winds and violent weather is much more common, and in the summer, density altitude can become amazing high. You will tire faster in the high country, especially since you are starting in Florida. I have used one of the cans of oxygen at 12,000 feet, and it lasted about 10 minutes, and did not do much good. Solo, it is much harder to assess hypoxia, than with a companion. My wife and I had a slightly difficult game we did every quarter hour, to asses each others mental acuity. 10.000 feet, we did fine most of the time, at 12,000, we could detect significant slowing of mental skills and awareness of the changes after 2 hours. Generally, I reduced altitude 4,000 feet to recover, as it goes away very slowly. If you go high early, your dissolved oxygen will be depleted, early, and when you reach the higher passes, you may be pushing your limits.
Be very flexible about where you are going to stop for fuel, and overnight. We flew from Maryland to Jax FL, Galveston TX, Mexico MO, and home, in 5 flying days. The first airport planned for each day was the only one actually landed at each day. Winds, weather, and fatigue changed the plan for the second and third, every day. We had no reservation for the only overnight that was in a hotel, and that stop was several hundred miles from our intended stop, deteriorating weather said stop now, just after noon. The three stops for multiple days at the named cities were the point of my trip, and the overall 2 weeks were the best flying trip ever.
A good plan is important, but flexibility in carrying it out is absolutely essential, or you will find yourself making potentially dangerous compromises.
That is a route that I would love to fly, and a 162 should do it fine with only one person and reasonable baggage. Have a great trip!
I agree with Murphy, in the mountains, GPS is not your best friend.