I have some tips...
When you clean the pots you can flood it first with a cleaner while you manipulate the pot vigorously, then use air and then contact lubricant. That way the movement of the wiper will clear debris while the fluid will remove it. You can also meter the pot before and during this process and see what progress you made.
Adding new solder (flux) can help make those type of joints easier to remove. Break sweat joints if required carefully with a small tool such as a screw driver and look for pin wiggle before removing.
When using your desoldering gun gently place it down on the joint to achieve melt, press the button and move the tip for a few seconds in a circular motion to manipulate the lead. Then lift the gun before releasing the button, this will reduce sweat joints and you can do a wiggle test before removing.