the sports button on the shifter does not change the transmission when depressed

Sometimes , that info can be found in the owners manual , if you're lucky enough to still have it , other wise , unless the Dealer still has actual paper service manuals (instead of only on-line info) might be able to find a trans shop , that has that info. 'SPORT' mode should only change the shift points , not the ability to shift to higher gears , to me , that speed and RPM almost sounds like the converter is not going into 'lock-up' mode.