He's a long way from you and not officially approved, but Brian Rodgers is as good as many. He is approved for Buzz Felten tweaks if that helps you.

Tuning problems are hardly ever to do with machine heads. There is enough friction in any machine head that it will not "run back" (ie unwind a bit in play) but it is always wise to make the final movement of the tuning key "upwards" to make sure there is no slack ("backlash") in the mechanism.

Is the problem constant, or worse after new strings? If so I'd suspect that the bridge pins are too tight on the strings and it is taking time and vibration to pull the ball ends in really solid.

Are you a string bender? Many finger pickers bend notes a fair bit with their left hand, and if that is the scenario, then Roj's theory about tight nut slots is a possible runner. A "checking" symptom for this might be if the guitar is a "clicker" - you know, you tune the string up, and it won't quite go up the last fraction to be in tune, so you try again and "click" - it has gone past and is now sharp.

You can also get clicking and unreliable tuning if the saddle has too sharp an edge - something quite easy to cause when trying to get intonation spot on. A sharp edge can lodge in the string windings or leave the fat bit of a winding wibbling on top of the saddle edge.

Is the octave spot on on every string? If not, when you tune you will be making compromises by ear which will be a source of problems when changing key.

Have you measured, with an accurate tuner, whether the instrument goes sharp at the first fret and the problem gets worse or better as you go up the neck? If it gets better, the nut is too high or a little too far from the first fret.

Could it be the truss rod or neck joint? Have you checked forward relief and neck angle before and after playing?

Is it better or worse with a capo? Check the old Rick Fielding posts about best practice with capos. If you are using best practice and the capo causes tuning problems you may find the neck relief is a bit high or differeing from side to side.

But if either of you sufferers give up and want to give the guitars away...