I did the Transam last year at age 62. I was only a "reasonably fit" rider, but I did it in 10 weeks of riding - due to job requirements I had to take a 7-week break in the middle, so I really did it in 2 5-week segments. Although I'm an older rider and not exceptionally fit, the "secret" to averaging 65-70 miles a day is simple; start early every day! Early gets you out of any city traffic before it gets heavy, early gets you several hours of riding while it is still cool, early avoids the intense solar radiation (sunburn), early gets the ride done before the afternoon storms pick up - the early bird really does win the prize! By early, I mean waking up at 4 - 4:30am and being on the road at 5-5:30 am.
WRT training, I would say 2 things; 1.) you need saddle time for all the normal reasons (muscle and aerobic conditioning), but also to condition your butt, hands, and feet (the contact points) and to break in a leather saddle (I'm a Brooks saddle fan and wouldn't ride anything else on tour), and 2.) to prepare you for the shock of climbing on a 80-100 pound loaded touring bike.
Before last year's Transam, I had never ridden a loaded touring bike. It's quite a bit different, and really manifests itself on the climbs. Ride the steepest hills you have nearby so you are prepared, because regardless of whether you start on the east coast (Blue Ridge about Day 3 or 4) or on the west coast (McKenzie Pass about day 5), you will be challenged with some serious climbing soon enough.
Read my blog to see what it's like - if you are going west to east, then start with my "second half" to see what you will encounter. Oh, it will be a blast and an experience you will always treasure! Best wishes,
www.crazyguyonabike.com/doc/BuddyHall