The next step up in Adventure Touring bikes are the Twins. The BMW's made this their own category over years, but are expensive. KTM has the 990 a perennial shoot out winner for big Adventure Touring bikes. Triumph has some, and so do some of the Japanese manufacturers. All of them are quite a bit more expensive than the KLR, but also way better for extended paved road touring. Less vibes, more power, more carrying capacity, more comfort.
If you aren't planning on going off road at least a bunch of the time then I would look for a multi-cylinder bike for touring. If you don't want to do dirt the big multi-cylinder Adventure Bikes still make great touring bikes, especially for long-legged dudes like you. But the singles, like the Kawasaki KLR 650 would not be a great interstate touring machine. Most touring cruisers would be far better. Not to mention purpose built sport tourers like Yamaha FJR or Kawasaki Concours. .
Good luck. The Adventure Rider site mentioned above is a great resource to do more research.
BMW 800 GS, a twin. Probably my favorite Adventure Sport bike. Plenty of power for whatever, but still small enough to be slightly manageable on dirt roads. I believe the BMW weighs about the same as the KLR, but has two cylinders and a bunch more HP. It also has all the bags available as (expensive) factory option.
If I could only have one bike, this might be it. (Or, maybe not, there is my Shovelhead digger...)