At 6'2" how are you having troubles with the height of the KLR? I'm 6' with a 34" inseam and am able to rest comfortable on the balls of my feet, darn near flat-footed.
If your requirements didn't involve so much highway or two-up I would recommend the DRZ400S. At right around 300lbs it isn't much of a challenge to throw around on a trail and won't throw out you back when you have to pick it up. The downside is that it is taller than the KLR by at least an inch.
I've ridden a DR650 on and off road, and while it is better than the KLR on the trails it is no better than the DRZ400S on the highway, and the DRZ will easily outperform either the DR or the KLR when the pavement runs out.
If I had to choose all over again I would still go with the KLR650 modified to be better for dirt riding. Any shock/fork work you would do to a KLR would still need to be done to a DR650.
2009 Kawasaki KLR 650 /// 2000 Suzuki DRZ400S