Interesting graph - thanks for sharing. It's good to see the independent variable (tire movement) on the X-axis and the dependent variable on the Y-axis - makes it easier to understand.
Also interesting that the curved line does not cross the origin (0,0). With changes in geometry, you can move that curve where you want. It might be worth trying to decrease the effect of the falling rate geometry at greater displacement - ie - move the curve to the right a bit. Also, the more linear section in the middle illustrates a range of movement from roughly -15mm to +10mm. That's only about an inch of travel. Can you try to add more linear displacement?
Lastly, I'm assuming that the graph does not show the effect of spring compression. It'd be cool to do that too - like show the effects with a 500#/in spring and then a 1000#/in spring.
I've enjoyed following your progress.