You spoke of taking the euclidean distance and subtracting 9.81 from that. That's not a vector subtraction. That's a scalar subtraction. That means you would not be integrating a vector. You would be integrating a scalar, completely ignoring the direction of the acceleration.
The point I was trying to make is that you need to subtract the 9.81 as a vector, leaving a residual vector acceleration and integrate that.
The centrifuge example would have a high scalar acceleration. Integrate that and you get a huge number. But integrate the vector and the directions would tend to cancel out over the long run giving a much lower number.
Did I make sense that time or am I still losing you?