The thing is Galaxie is that when you shift manually when you get to drive there is no difference. The 2-3 shift is always done with the manual valve at the "D" position.
Now if I was running a car thru the gears manually I would tend to run it out a bit more in each gear and have the throttle open wider. This causes more govenor pressure from the road speed, more line pressure from the modulator seeing less vacumn and more line pressure from the pump spinning faster. The shift will be firmer if there is issues inside the tranny with leakage and adjustments.
Shifting automatically are the shift points quite low? Will the tranny shift harder if you lean on it harder shifting manually?