Flush the transmission first. I've fixed a bunch of cars like yours without replacing any parts. Most were due to the coolant contamination issue but a few simply had dirty fluid which affected the performance of the TC lock-up clutch. This is what causes the droning/jolting you're experiencing. Expect to pay a dealer around $400 to do this job.

There's also a chance that the transmission ECU is to blame, but you'll need to erase the transmission adaptation data and then see if the problem goes away. If it does, the ECU is at fault.