Please have a look here:
I have used your key positions and placed a Null-Object combination of each under a Cloner, then via Modify Clone, created the animation needed. The Random-Field and its Ramp animation will drive the “show” the steeper the “Curve”, the shorter each animation will be, the faster the progress of the whole, the faster it will go through the set.
To my knowledge, there is no option to inherit and randomize the starting points while not changing the animation speed.
I hope that will work for you.