My working single mom made many dinners this way. Us latchkey kids would come home, she might leave us instructions - add / check / adjust knob setting ... that was it 'till she got home, then ... dinner.

Ants killed two GFCI outlets where I live. The buggers like the tiny extra little bit of heat the electronics in there generated under load ... that was all fine until the ants got a bit too cozy and dense across 120 VAC.

>This is a problem with the lights, not the outlet

Could be either at this point - insufficient data to conclusively determine.

>GFI outlets don’t trip based on moisture, they trip on a difference in the current between the line and neutral.

Get enough moisture between hot/line and ground, and you'll have that difference in current that'll trip the GFCI. That principle may also save someone's life - e.g. wet feet in bathtub, hand on faulty device plugged in that contacts or leaks hot to the person's hand, flows through them, into feet in tub and ground ... again, moisture, current imbalance between line/hot and neutral ... and ... it trips.

Try a fairly heavy load that's compact and highly well insulated from ground - just hot and neutral and well insulated with nothing for it to leak off to anywhere nearby. If it still trips the GFCI outlet, you probably have a faulty GFCI outlet. Various intrusions can cause them to fail, e.g. moisture, ants(!), ... also possible, though less likely, that the GFCI circuit itself might be faulty, or there could be some wiring issue that's causing it to trip (e.g. by causing excess heat build-up from poor connections or faulty components).

screw extractor

In more detail: center punch, drill, screw extractor

And as others suggested, probably good to let lubricant try to soak in for some while first.

Anyway, I learned of and used this method over two decades ago, when I had a bicycle handlebar stem bolt that snapped.

Probably very similar to how lengths of cable are measured. It's generally pressed to a metal wheel with a flat outer diameter, and with reasonably appropriate accuracy in machining and such, length is measured with that - often with a counter (and reset button) attached to that wheel. Mostly just need to reasonably well press cable to the wheel as it's drawn across. Well, string would be fairly similar, reasonably well press string to metal wheel like that as the string is drawn across.

Could also do something like accurately measuring circumference of some suitably designed wheel/hub, running the string around that one full turn then off onto something else to be spooled (so it doesn't get fatter with string piling up), and carefully measure it's rotations (and start and end angle of rotation). Probably not too horribly complex to do something like that, and may not be as sophisticated, but may be a much easier set-up ... with a suitable wheel/hub and mounting, and string routing means and procedures.