The behavior of this Hydra-Matic transmission is the way they all behaved. Changing the oil may help your automatic shifting up and down thru the gears, but the action to get in reverse is the way it will always be. It wasn't until the late 50's the easier reverse was put into play.
To obtain Park. just shift to low, hesitate, then pull into reverse, and turn off key.
Voila-park position.!