Sorry for the delayed response. Couldn't get off the phone yesterday. Anyway, adding a CSV may stop the water hammer on pump shut off. But if you have a check valve sticking, the CSV may not solve the problem. When a check valve sticks in the open position, sometimes the water flow has to completely reverse to close that check. This is what causes the loud "thump" you hear after the pump shuts off.
The CSV would reduce the flow to 1 GPM to fill the pressure tank. This would normally mean the check valve is only open the thickness of a piece of paper when the pump shuts off while only pumping 1 GPM. Then the check valve would not slam on pump shut down. If the system would have had a CSV from the beginning, the check valve would still be good, as it would not have slammed itself to destruction in the first place.
But since the check valve is now sticking open, it may still stay stuck open when the pump is only producing 1 GPM, until the pump stops and the flow reverses. It is about a 50/50 chance of the CSV solving this problem after the check valve has been damaged. You may still have to replace the check valve.
The pump/motor cooling is just the opposite of what you are thinking. The pump/motor pulls less amperage and runs cooler at 1 GPM than at higher flow rates. With a CSV you could run 1 GPM from a hose, and never shut it off for the rest of your life, and the pump would run cooler and last longer than if pumping higher flow rates.
I don't know if the CSV will stop the water hammer from your damaged check valve, but it would certainly help, and would keep that from happening again as well as making the pump, tank, and everything else last longer as well.