Not sure if you got an answer yet;
soft 1 - 2 shift is a control of multiple things,
band adjustment will not help a soft shift if the adjustment is close to correct.
Shift firmness of 1 - 2 shift is controlled by : servo size, the band lever fulcrum angle, the accumulator spring in the valve body and the main line pressure.
There are several different size servo pistons for the C6
The band lever is replaceable and there are several different levers with higher apply angles for more holding power on the band.
Main line pressure; higher is a firmer shift.
1 - 2 shift accumulator in the valve body usually has broken OEM springs in an old C6 unit. Many shift mod kits block this accumulator in place or provide stiffer springs for the accumulator.
The detent lever affects the shifts at different apply of the throttle depending on the road speed of the vehicle , main line pressure, and level of vacuum the modulator sees at that moment. They all work together to affect shift timing or down shifts.