On my Glashütte the phenomenon however doesn't seem as big as on standard electronic trimmers.
When adjusting those on the kit clocks I've used pliers on the screwdriver as not to move it too much. Great care is still required. That's exactly why I have thought about making a dedicated tool. A screwdriver with a rod across. First turn it gently by the shaft until it's not moving anymore (to remove slack between screwdriver and slot). Then turn it by the rod a barely visible amount. Then you've overcome the threshold while ensuring it's not moving a lot.
In watches space can be a problem but in marine chronometers there could easily have been two trimmers. A coarse and a fine. The coarse for adjusting like +/- 1 sec/day and the fine +/- 10-15 sec/year and thus minimizing the problem.
Also digital adjustments also have their drawbacks too. It uses flash memory which with enough time (depending on design/mask size) will suffer from bit rot. It's not a big problem if it's only the adjustment info stored in flash as it can just be rewritten and en eon will pass before they're worn out physically (yes flash _is_ worn physically!). However today the program for the µC are also stored in flash and that can potentially be a huge problem in anything from 10 to 200 years. Making the program in mask rom is practically not done anymore. Many of the popular µCs like Atmel are only guaranteed for 10 years data retention(!) Microchip also a popular brand usually have their rated for 40 years.
So it may very well be when we're old men sitting in a nursing home then our old watches and clocks with trimmers are working flawlessly while those with digital technology has stopped working for an (most people) unknown reason - but the explanation is simple - "bit rot". That is the charge in the flash cells have "evaporated" (just the electrostatic charge holding a balloon to the ceiling) and so the µC has lost its program. And like a computer it's useless without.