So it turns out the delay was caused by "Has exit time" being clicked in mecanim. It must've been waiting for the idle loop to finish before moving.
I look forward to seeing what you come up with in 1.50 :)
Also I really can't get my head around the destination accuracy. The capsule collider of my character is 1 tall and 0.5 but turning the accuracy down seems to give better results than turning it up.
It seems impossible to get the character to land…