I am not a mechanic now, but when I do a front brake job, I also check the calipers/pins and lube them. And as stated, it is unlikely that I don’t change the rotors, only when I am 100% sure they are fine. It is not worth it.
“Personally, I still think the rotors are the ultimate cause of the vibration
But I do agree with your methods, regarding cleaning and lubing
Not doing that is asking for trouble . . . I’ve seen more than a few brake problems caused by poor work habits, such as not cleaning and lubing” @db4690, Then it seems we both agree that the remedy is to replace the rotors and do the thorough cleaning and lubing before reassembling everything. CSA
So, ultimately the rotors are the cause of the vibration and the sticky calipers (and excessively worn pads?) most likely caused the uneven wear on the rotors.
Already got a line on a pair of rotors from RockAuto. I never knew about lubing the pins, nor that such a small variance in thickness could have such a huge impact.