Hard shift/kick and jerk taking off

There are two possibilities here. The first is in the kick-down circuit, while the other is in the torque converter. I suspect the problem is in the kick-down circuit (it’s my shorthand). Here’s what I think is happening. When you press the accelerator (your Chevy uses a computer-controlled ignition/fuel-injection system), a signal is sent to the central control computer telling it to tell the transmission computer to shift down a gear so that the torque quotient and power output are increased. To do this, your solenoids have to fire correctly. I suspect the solenoid combination that enables the passing gear mode is failing (you said it was intermittent). No, the device hasn’t totally gone or else your Chevy wouldn’t be shifting correctly. Instead, the solenoid is just getting flaky and should be replaced. Which one should be replaced? It is hard to tell as there are at least two control solenoids in your transmission. If your started by having both of them replaced (about a $500 job), I think you will see the problem clears up.

On the other hand, it could be a torque converter problem — something to look at if the solenoid fix doesn’t work. One of the vanes on the torque converter may be bent or slightly out of alignment. These symptoms increase in severity when the transmission is cold and begin to ease up as the tranny warms. If you have to replace the torque converter you are looking at a major teardown and likely an $1,750 to $2,000 bill.