The slop, or "play" seems to be in the tuner worm gears themselves. Just years of use have created play that I cannot reduce by simply tightening the button screw.
When rotating the button, it will rotate say 10 deg before rotating the string post shaft in either direction. Very frustrating.
It is just time for some new tuners that are drop-in replacements for a 1980 ES 335 where I don't have to drill any new holes.
I just can't find any with tulip style chrome buttons.
Or - if anyone knows where I could ship these tuners to a tuner reconditioning guru - maybe someone is out there.
I can buy a used set from eBay, but those may be just as worn and sloppy.
John