Lube both ends of the cable where the barrel connects to a lever or arm.
Also, some bikes have parts like a cross shaft and/or cam that can be polished...that will make it operate more smoothly.
Are there major grooves in your basket?
Can you run lighter springs and/or less stack height without the clutch slipping?
Use a fairly long lever and move the perch in on the bar so that you have more leverage. Don't forget to put teflon tape between the bar and perch.