Despite breaking an REI Randonee on the first day of my trip (starting at 265#), the last 4400 miles went fine on its replacement (another Randonee). Any touring bike should be fine -- just stay clear of the racing bikes with thin tubing. REI Randonee (if you can find one) or Safari, Surly LHT, Trek 520, Cannondale touring series, Jamis Aurora -- any of them should work just fine.
You may have problems getting one this late in the season. Most manufacturers make a limited number of touring frames every year. They'll hit the showroom floor in March, and often be gone by the end of May.
Let me (strongly) echo the advice to get the wheels tensioned. Most of these bikes, ~$1,000, will have machine built wheels. They may be true, but they're not tensioned high enough, and the spokes will start breaking between 200 and 500 miles. Find a good wheelbuilder, tell him what you're doing, and pay him to bring them up to tension. It'll be the best money you can spend before leaving!