Your Kona Sutra isn't a bad start. If you've got the new bike itch, look at the Fuji. Otherwise, you might want to look at slightly smaller (and lighter) tires that what's stock on it. Panaracer Pasela 700Cx35 would be my choice.
As John noted, you'll likely want low gears; if you ride long enough, you'll hit a long day with one nasty climb at the end of that day when you're tired from climbing, headwinds, long hours in the saddle, or some combination. That's the day you'll want lower gearing than the typical 1:1 (27 gear inch) low. Since you're looking at a supported ride, you may get by with a 23-24" low, but if you can arrange 20", that would be better. Also, taller bars are typical of touring bikes, like the Sutra/LHT/520. Finally, interesting places to ride often are not the ones with the best roads. Bigger size tires, and heavier tires, soak up some of the road shock and prevent flats. (Having stood on the side of the road as the rain started waiting for a SAG after a blowout... No, I'd rather not repeat that!) I've settled in on 32 or 35 tires, although my lightest bike is limited to 28s, as my preferred size.
A touring bike has the lower gearing and higher bars you won't get with a typical carbon fiber road bike. The Fuji feels lighter than the LHT and 520. (I've never ridden a Sutra, and I've only seen one in person, which is fairly normal for most touring bikes.) But bike weight isn't the end-all and be-all that some say it is; add a way to carry sunscreen, emergency rations, rain shell, spare tube, patch kit, pump, and enough water to get you to the next SAG stop, and your featherweight bike is heavier than the naked tourer. Also, remember what does count is total wheel weight: add luggage weight and your weight to the bike weight, and what's the percent difference? Finally, you'll have frame clearance for wider tires with a touring bike than the CF wonder bike.
Now if you've got the money (and time), you can get a custom bike that's a relaxed or sport touring frame, and "old mountain" gearing with a triple and really low gears. That'll take perhaps 5 pounds off your frame, and $3-4,000 out of your wallet. Gear down and spin the extra weight up the hill might be the better recommendation.
