That transmission is VERY sensitive to throttle pressure adjustments. If you disconnect the TV linkage at the side of the transmission, you should be able to move the lever through its range of motion. You'll feel a spring loaded detent near the full travel position that's the forced kickdown (passing gear) that causes the 4-3 downshift as the throttle reaches full open. The geometry of the throttle linkage also has a pronounced effect on part throttle downshifts. The 1-2 shift happens very quickly, at probably less than 5 MPH, and even when the TV pressure is right, there will be a somewhat rough 2-3 shift. In the late 1950's the Hydra-Matic got the nickname "Jerk-O-Matic" because of that rough 2-3 shift. Contact FATSCO transmission parts in New Jersey to see if they know who might have the adjustment fixtures for sale or rent.
Jerry