First you need to find out why it's overheating. Are you in a cold climate where the water only could have frozen and cracked the head or block? If not, then yes I would flush the system with radiator cleaner (never heard of someone using the CLR, but that doesn't mean you can't). Maybe there is build up in some of the smaller passages or smaller hoses?? If cold climate, then are you loosing any coolant?
Is all of the air out of the system?
How old is the water pump?
Timing correct?
Maybe try running it without a thermostat and see if it runs cooler, then put in another one, I would use the standard temp one also. Screw the gas mileage, how much would it save anyway (especially if you blow the motor)?

Then when you get it running at the right temp, start diagnosing the fan operation.