(This answer was rewritten after the questioner rewrote the question)
If we do not change any properties nor the placement of the camera, the only theoretical solution principle is the following:
for every moving point and all three XYZ world coordinates calculate the following formula
P = Po + ((Po - C)/Dv) * V * t
P = the xyz coordinate of the point at the moment t
Po = the initial xyz coordinate of the point
C = the xyz coordinate of the camera
Dv = a constant, the distance where the escaping velocity should be =V
V = a constant, the effective escaping velocity in the midpoint of the image, negative V means moving towards the camera.
t = the running time, 0 = the start of the sequence
The same without any formulas: Keep the placements relative to the camera proportional to the time, every point moves to the direction which it initially had in relative to the camera and the velocity is proportional to the initial distance between the point and the camera
The points move towards the camera and they reach the camera at the same time. That time is Dv/V; to get positive time, negative it, if V is negative.
NOTE: there's no need to have constant V, it's enough to use the same V in the calculation of one frame.
I have no 3D animation software. Thus I have no idea how to program this to Cinema4D. Sorry!