Well, I started this morning by removing the brake pads and then testing for the noise and sure enough I heard nothing. So, I dismantled the caliper and piston, gave all the parts a serious spray with brake cleaner and the noise is gone. I think it ultimately wasn't that the piston wasn't retracting, but that the side-to-side play of the caliper had frozen up with gunk. It moves much more freely now and allows the pads to grab the disc evenly on both sides, which I think was the reason it was making a racket in the first place.
Thanks for the help all and Happy New Year!
'81 CB750K, '70 C70. As long as the Honda's older than I am, I'm happy...