"we get a downward force of 23,104N vs. an upward force of 3960N, which results in a downward force of 19,144N"
this is incorrect.
newtons third law says "When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body."
so, if the top block hits the bottom block with a force of 23,104 N, then newtons third law says that the bottom block will also exert an upwards force of 23,104N on the top block.
I'll use an example to hopefully help you understand where you are getting it wrong.
Take a 50lb weight and gently place it on a scale. How much does it weigh?
Take the same 50lb weight and drop it 5ft off the ground on top of the scale. At the moment it decelerates after striking the scale, does the weight change in that fraction of a second?