I have been a certified mechanic since 1982 and I know of no way to be able to tell a customer "it is working fine and strong".
I believed the fan clutch was working perfect on many overheating vehicles but after I changed the fan clutch the problems were solved.

 

At 289K I'm amazed the water pump & fan clutch are still working. If you've already replaced the rad & t-stat why wouldn't you do the wp & clutch? Don't try to save a nickel after you've already spent a dime. And flush the system thoroughly. Get a flush & fill kit from your local parts store for about $10. Splice it in line with the heater hose & hook a regular household water hose up to it. Works great.

 

Updates????

 

If you haven't already done this, put a radiator cap on, new or not, let the thermostat open and let the water flow for 10 or 15 minutes, then feel the radiator for even heat. First check if the top of the radiator is hot and the bottom cold. If they are the same to touch and hot then look for cold spots anywhere. Depending on your radiator you might also have to compare the front to back. Probably not, but maybe. What type of radiator did you get? Crossflow or downflow?

Also, did the shroud fit the new radiator the same as it fit the old radiator?