After updating the original post to include Newtons, I re-verified the natural frequencies and added the new ones using the racing aspirations calculator (
LINK
f_nat1 = 1.3 Hz front, 1.5 Hz rear
f_nat2 = 31.3 Hz front, 22.1 Hz rear (stock pressures)
f_nat3 = 9.03 Hz front, 8.08 Hz rear (stock pressures)
From this, we can infer that there is some small interaction caused by the tires at stock pressures. Bumping up the pressures to autocross level (10000 lbs/in rate):
f_nat2 = 30+ Hz (autox pressures)
f_nat3 = 11.1 Hz front, 9.9 Hz rear (autox pressures)
Now we see that the tire's natural frequency jumps up ~23%, which decreases it's involvement in the bounce dynamics of the car. The added pressure also decreases sidewall flex, which maintains a more even contact patch.