Before you go to the extreme of getting an expensive overhaul, consider doing preventive maintenance and adjustments on it. There are two band adjustments, and throttle pressure linkage that connects a lever on the transmission side cover to the carburetor. Adjustment of all these items is critical to good shifting. The HydraMatic is a 4-speed unit with a fluid coupling, not a torque converter. The 1-2 shift will happen almost as soon as the vehicle starts to move, usually at less than 10 MPH. 2-3 and 3-4 shifts will happen according to throttle opening and road speed, and the throttle linkage adjustment is very critical. Shifts will be firm, and there should not be any RPM flare-up between shifts. Maintenance and repair manuals are usualy available on Ebay for reasonable prices, and it's good to have one. These transmissions were used in Oldsmobile, Cadillac, Pontiac, Chevy and GMC trucks, Nash, Lincoln, and certain models of Rolls-Royce. They were also used in WW II tanks, and US military 2 1/2 ton trucks. Once it's adjusted correctly, I think you'll like how it drives.
Jerry