My stock clutch ONLY chatters at low RPMs (or idle). The more throttle applied at low RPMs, the more chatter. If you're getting on the throttle at all while at 1200 RPMs (in any gear), that is lugging and definitely causing the chatter. The Z likes high revs. I make casual shifts around 3-4K RPMs, meaning my next gear engages near 2500 RPMs or so. Shifting in this manner virtually eliminates all chatter on the stock clutch in every gear except 1st.
You're just fine at 20 mph in 3rd gear. The owner's manual says you can be in 6th gear at 35 mph. I definitely don't make it a habit, but I have done a 1st to 6th shift before