Thanks Radd and Frayed Not.
I've been changing strings on my guitars for a looooonnnnng time, and do have a procedure indeed, so that advice is spot on. When putting the string ball in the saddle, I just put enough string in, and then push it with the saddle pins. I do tug on it but only with my hands, so I'll try using pliers.
To ensure I have enough wraps I do this. I insert the string through the tuning pegs, with the tuning peg hole in-lined with string's slot on the nut. For wound strings, I grab it from the nut and pull it back so the point where I grabbed it from is 1-1/2 frets back; for unwound strings, I pull it back so the point where I grabbed it from is 2 frets back. This has given me at least 3 winds for the wound strings, and at least 6 winds for unwound strings, as Frayed Not recommended. This has always worked for me.
My tuners are fine, nut and small screws are snug.
I'll try to lube the nut and bridge, though I don't hear the string "popping" when tuning, which usually is the indication for a nut or saddle binding the string.
Thanks.