I've owned multiple KLR's and the big Strom. I got talked into trying the V-Strom because of all the owner-riders raving about how it was the poor man's replacement for the big GS.
If the big GS is as tough to pick up when loaded as the V-Strom, I would recommend against riding alone for any long trips.
And the Wee-Strom is only about 25 pounds lighter.
As for the KLRs, I found them to be the most comfortable bike I have ever ridden, ergonomics wise (I'm 6 ft, 210 lbs, 32-inch inseam). The trick to getting along with the KLR's seat height is to use the left peg like the stirrup on a horse saddle. Put your left foot on the peg, rise up on the peg and then swing your leg over; let the bike settle under your weight, then raise the kickstand. This allows you to set the suspension on firmer preload for good ride, but not 'pull your groin' as you so clearly stated in your post.
Now to the Versys: Compared to the KLR, I love the power and smoothness of the twin; torque is about the same due to similar displacement. The sixth gear is nice,
and the bike is very flickable. I prefer the flat seat of the KLR for moving my butt around on long rides, and the extra fuel capacity is nice, but not mandatory for riding in the U.S. Easier for a do-it-yourself mechanic to work on the KLR (carburated bike), but the fuel injection of the Versys suits me just fine. More aftermarket farkels available for the KLR, (it's been around longer) but the Versys is catching up, rather quickly.
So I would say, for you, decide what percentage of off-pavement you want to do, and whether you want to do any single-track (KLR would be better choice for it, although not the perfect choice).
Whatever you decide, ride and enjoy.