I think the load deflection curves are just another way to present the tire spring rate numbers. Missing is the lateral force vs slip angle data which is one of the most common forms of tire test data.
Without knowing the tire spring rate of your old tires and the R888 I am not sure how your make a beneficial wheel rate change. Note that tire spring rate measurements can be done statically or dynamically on a rolling road.
What is considered the major contribution of the wheel rates to car performance: contact patch compliance or tire temperatures?
Brian