Back to the question. If the OP considers himself to have "reasonable cycling fitness," saddle time will be the hardest hurdle. Lots of people go on their first tour figuring on averaging 15-20 mph, and most people come off that first tour having averaged 10 mph. 50 miles per day average will get you across the country within three months, but that takes 5 hours of riding a day. So start now, get out and go for long rides as often as you can.
I'd also suggest reversing the direction of the ride because of the weather and the season. The first half of the trip headed west, expect temperatures in July and August to exceed 90 degrees F almost every day, and you'll probably top 100F for a week or two, with enough humidity that you'll be soaked in sweat. If you start out west, you'll hit higher altitudes, and cooler and drier weather, a lot faster. If you decide to stay with the westbound direction, try to ride at dawn for cooler (and less windy) weather.