*Update*
I finally got the new radiator installed. I also replaced the water pump because there was white crust in the weep hole of the old one. No detectable leaks so far.
I'm so glad to have replaced the radiator because the old one was dirty, rusty, and the coolant that came out was dark and grimy. (petcock was stuck, so I never could drain it properly)
Here's the real trip: My engine runs 9 DEGREES COOLER. The thermostat is designed to open at 195 degrees, and as soon as the coolant temp reaches 195, it starts going down again. It used to top out at 204 degrees. I imagine the dirty coolant and heat contributed to my water pump's early demise.
As it turns out, the chirping/rattling noise was nothing more than the manifold heat shield being on loose and/or crooked. That explains why it only occurred as the engine warmed up and at low RPM (my engine vibrates a bit below 1000 RPM.)
But, the seemingly impulsive, unnecessary repairs turned out to be necessary, so I guess I got lucky.
Thanks again for all the advice.
Jonas