R6, when's the last time you had an oil change? My shifter gets really harsh after about 1500 miles, so I do an oil change every 1500.... Also, something to keep in mind, and you might want to look up manual/sequential transmissions on howstuffworks.com: when you skip gears like that the RPM's drop significantly right? which means you're using more of the bike's torque than horsepower, which means it's really binding up those gears (not a bad thing, it just is).
Try giving it a quick blip to raise the RPM's maybe 2-500 then quickly back off the throttle while you pull in the clutch... This will free up the gears and "float" them, so when you engage they should still be spinning plenty to shift, but not be caught on one another. Give it a shot, let me know.