There is a valve that spins as fast as the axle and when the centrifugal force overcomes the spring it moves and allows it's fluid to shift from first to second, and 3rd. $th has a switch controlled by the computer if you have an overdrive with 4th speed. The pressure that must be overcome gets greater when you press the pedal, the more you press the greater the pressure, that's why releasing the pedal allows the other(governor) valve to shift. That gas pedal pressure is passed through a cable. It's too much, too short so it moves the lever more than normal. You need to try to make the lever it moves not move as you give it gas until that cable with the pedal travels 1/8th of an inch of measured cable. Less throttle pressure may help or the governor valve is having to spin too fast to allow the force to move it. You can replace that governor valve by taking just the tail-shaft cover off. So first check the fluid because that decreases pressure when low, and if dirty try servicing it, dirt may have gotten the valve in back stuck. Try shifting using D1, D2, D and if ok the valve body the pedal cable operates is probably ok. You may need to try removing that gas pedal cable, if it up-shifts too fast you know that's it.
If it became kinked that would make a late shift. It shortened, pulling the throttle pressure valve more than it should. The shape and amount of fluid is everything. It is still using a speed sensor for overdrive and the speedometer only in 98. Everything else is non-electric.