I demoed the K12S in Vermont and found the same problem. My actual comment to BMW was "This is definitely not your father's K-bike, well...except for the clunky transmission". The clunky trans seemed no different to me than the clunk on my K75C or any other K I've ridden, K12GT, K11RS, ect. Without making ANY mechanical adjustment on those bikes but adjusting my shifting technique instead I was able to shift sans clunk. I applied this technique to the K12S demo bike and it solved the problem just as with all the other K's.
What to do:
When riding bring the RPMs up to where you want to shift. Nothing special here, just get the RPMs to that optimal spot. As your bringing the RPMs up (a second or two before you shift) take your shift toe and put a bit of 'pre-load' on the shift lever. By pre-load I mean just a little upward pressure on the lever. Don't shift or knock it out of gear, but put it right on the brink.
Next, when you're ready to shift, crack the clutch lever just enough that the shift lever falls into gear. Release the clutch and go, go, go. Cracking the clutch may be a just little squeeze or it may be half a pull depending on the play in your clutch. There should be no reason to pull the shift lever to the grip. That causes a pause where either RPMs drop -or- the bike get in gear ok, but there is a pause before getting back on the throttle.
This technique will not damage or harm your trans, clutch or whatever. If you try it and you grind gears or have some other undesirable result try again, paying closer attention to what your doing. It's a technique based on feel (shift lever on foot, RPM peaking, clutch to hand to foot to shifter) that doesn't take long to master, but takes a while to make habitual. I suggest taking the long way home from work and trying it. When mastered it is a short, concise and quick but FLUENT and SMOOTH method that enhances the shifting on any bike (I've used it on R-bikes, Suzuki, Kawasaki...). It also puts you in more control of your bike by trimming off the slightest of a second and making the bike MORE RESPONSIVE TO YOUR CONTROL INPUTS. And like the Hokey-Pokey, that's what it's all about.
My father (who taught me this technique and uses it religiously for the past 100k miles) likes to tell a story about how, on his way home from work on his K11RS, he was zipping from light to light at a spirited pace (must've been the Friday of a rally weekend). There was a guy in a car in the lane next to him going the same way. After a few miles they came to a stop light and the guy in the car gets Dad's attention and asks him (with a look of amazement and slight confusion :wtf ) if his bike is an automatic. 'Nuff said.