You can improve you z speed by decreasing your step rate, it works great all the way down to quarter or even half stepping. Full steps are kinda rough. No problem, but 30mm/s not gunna happen. Too much inertia on large moves. You just want faster accelerations for small moves.
Go to half stepping and torture test your zaxis to increase the z max speed to maybe 12-16mm/s and accel as high as you can go before loosing steps. I have some torture test scripts on here.