Good luck if you get underway. The advice you have read here is just about it. I would add there are lots of out-of-the-way places like country churches that have a water hose out back where you can get showered well at night. Perhaps you're not supposed to do that. I don't know. I have many times. John Nelson is right on with his advice; however, I will not go without my Cytomax and a steady supply of it mailed forward. Also, I must have a beer occasionally.
It looks like I might be doing a transcon after this June 2013. Our times are out of sync. Depending on your route, you can carry only a very light blanket, and if on the ST you might get by with using it as a pillow. I will most likely do the ST. I prefer not to do it in summer, but that seems to be the hand that destiny is dealing me at the time.
Perhaps my next comment is out of line. I do not believe you should do any route hauling a 65-pound dog. The Atlantic coast is the only route for that because it is compartively level.
Any well made bike frame will get you there. Used ones are available for a song. $250.00 will put you in the way of all new components you need to add. Not top of the line but definitely functional. Probably $300.00 total, around 1 / 4 the price of a SLHT. I have been using the same old Raleigh frame for years on long, strenuous tours. No problem whatsoever. When it is time to go I get new pedals, bearings, wheels, tires, tubes, brake pads, chain, freewheel, spindle or cassette, maybe a deraileur. I get there just as quickly and efficiently as anyone on a $1200.00 bicycle. It's doable.