I'd take at least 5 days to get there, but then I have bad knees and a bad back. A 500 mile day is as much as I want to do, and I've done it a few times. I wouldn't want to do 500 mile days 3 in a row though. Personally, I'd plan on 350 mile days in the saddle, but then I'm not into superslabs, so I'd map out a nice back highways strategy. I also take a lot of small breaks...every 75-100 miles. That helps me from getting stiff. 350 mile days also allow some time to stop along the way to take pictures. If you want something to remember the trip, taking lots of photos is the way to go, and that takes away travelling time.
I don't know how much riding experience you have, so the rest of this is dumbing things down a bit. A lot of this depends on your personal stamina. Have you taken any long rides? What's the longest day ride you've been on where you didn't feel wiped out at the end of the day? These are the types of questions you should be asking yourself. And build up some of that stamina before the ride. Go on some long day rides building up to 300-400 miles before you go on this trip. Take an overnight or weekend trip. There's nothing worse than being out on the road and having your back act up, because it's not use to being in the saddle that long.
