To add to all the advice Dave has offered, there are a couple of actions you can take. Rather than taking a power nap, take a walk. Even in a rest area you can walk around the whole place three or four times. Tiredness during the day is purely because you are not getting enough oxygen in your blood/to your brain. Walking gets it all circulating again. If you do not fancy walking round and round a rest area, stop in the next town and go for a walk. No knowing what lovely sights you may stumble upon, or interesting folk you may meet.
Another thing you should do is drink lots and lots of water. Not coffee, not coke or any other sort of fizzy drink, but pure plain water. You can usually pick up a slab for not very much at all. Check the supermarkets wherever you are.
You should also do some reading about the country through which you will be travelling. Its history often makes for very interesting reading, especially if you go back as far as what was there before Europeans arrived on the continent. For example, when I drive across the vast expanses of the middle States, I reflect on those who live there and who provide so much of the food for the country. What must their life be like? so far from the services we city dwellers take for granted, Often without the continuous access to all modern requirements you and I regard as essential. I think of the pioneers who opened up this land, and the hardship so many endured. I think of the native settlements which were disrupted when white man arrived. I wonder what it all looked like two thousand years ago.
I don't have time to notice the black top with the white line down the middle which is the main cause of road hypnosis. Travel changes people and educates them to different ways. Be sure your three months are not wasted.
Lifey