no dexron III is compatible with T-IV, - toyota T-IV is a HFM ATF which is a bit more modified than Dexron III-H.
Harsh engagement can be a hydraulic fault or an electric fault, Find a proper mechanic who can decipher the data being seen on the scan tool.
If you are getting a slam into 1st from N or P, the forward clutch maybe sticking, you will also feel the shifts being too stiff (almost honda type), this can also be caused by too much noise in the electrical system.
Best is to find someone sensible who can use the data being seen on a scan tool, most mechanics in pk just use it as a reader and then throw parts at the car while praying it works.