These boxes do shift, shall I say, firmly from 1 to 2, especially when they're cold. The fact that the 3 to 4 shift IS smooth proves the vacuum shift modulation is working as designed. That leaves the throttle position linkage to be checked and adjusted if necessary.
On the top rear of the motor you'll see throttle linkage that's connected to a rod or cable that goes down to the right side of the transmission. The top end of the rod or cable has a ball socket; use a flat blade screw driver to pry that ball off its respective linkage pin.
GENTLY pull the rod or cable to its limit and GENTLY allow it to return to its "natural" position - the position at which it stops. Then, without you pulling or pushing it see how it aligns with its pin - it should attach to the pin in that position - no pulling or pushing. If it doesn't align with its pin you should lengthen or shorten the rod or adjust the mounting nut of the cable so it does align. Then put a bit of grease on the pin and snap the ball onto it. Done, the transmission is now exactly coordinated with the throttle position and will shift accordingly, but not necessarily smoother.
Remember these old boxes were designed about 30 years ago and are 100% hydraulic whereas we've become spoiled by electronically controlled transmissions that even momentarily retard the (gas) engine ignition to achieve very smooth shifts.
So as an aware driver just let up on the throttle and it will shift without snapping your neck!
And if you want to get into gruesome transmission subjects research the B2 Servo and see if it applies to your transmission. Try
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