Video: Should my kickdown have this much play?

The play down at the bottom is fine, and means almost nothing.
To set the KD, requires the engine to be shut off and the throttle to be wide open at the carb, and the gas pedal to be on the floor. Both of these,not one or the other.And it has to stay there. Then you push the link rod down or back, as far as it will go, hard; and keep it there. Finally you take up the slack on the adjuster, until it just slips onto the correctly located KD stud.If you cannot make this happen then one of the parts is not right. Either the lever at the bottom is too long or the anchor on the intake is in the wrong spot or the linkrod is the wrong length, or your carb linkage has not been Moparized. These are all possibilities if the engine has been converted from 2bbl to 4bbl.Finally,secure the adjuster, release the lever and return the carb to curb idle.

Now if the automatic shifts are not high enough for you, then you will have to crank down the governor pressure, or crank up the line pressure.But since it is already banging the 1-2, I would go to the governor.If the shifts occur at different rpms, then one of the shift valve springs will have to be changed.If you cannot get the shifts high enough, you will need a different TV spring. All these parts come in a shift kit;plus many more changes

Messing with the band adjustments does not achieve the results that you are after.