while the extra centripetal acceleration draws blood out closer to my fingertips.
I think you mean "centrifugal force". Note that a centripetal acceleration/force would be pulling your blood back inwards from your fingertips; you're looking for the equal and opposite force that is pulling the blood away.
Physics teachers who say that there is no such thing as centrifugal force are lying; it is every bit as real as gravity. It is a white lie, with the point of avoiding accelerating non-inertial reference frames. Such physics classes will show that centrifugal force is entirely explained by inertia in a reference frame undergoing centripetal acceleration. That's great.
Here's the problem: those same classes will regularly describe gravity as a force. The thing is, once you study general relativity you realize that gravity (and in particular the 9.8 m/s^2 acceleration you feel downward) has exactly the same explanation; space-time is curved by the mass of the Earth such that the surface of the Earth needs to accelerate upwards at 9.8 m/s^2 in order to remain "in place".
In other words, centrifugal force is entirely as real as gravity. If it is centrifugal force that makes your blood move out, don't be afraid to say it.