I think the residual coolant is not really under much pressure, it simply is draining to the low point by gravity.
I don't have trouble with coolant making things sticky, really. Do you have a tramp oil skimmer in the sump to remove way lube oil? That tramp oil can add to the stickiness factor.
If you allow the tapers to get a good wash at every tool change, they should never get to the point of being sticky.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)