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I have an Atmos clock on the mantlepiece but as the article alludes to, although it is perpetually in motion it does not keep time very well.

I love it as a mechanical wonder but I would love it more if it were useful as a timepiece.

I've been trying to think of ways to measure it's timekeeping such that I could make the necessary adjustments to fix it, but it's also so delicate that I'd rather just leave it alone.

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At least for some form of mechanical clocks: There is an app for that :)

E.g., for Android, the "Watch Accuracy Meter", which can be found in the Play Store or the APK source of your choice, uses the phone's microphone to measure the frequency of mechanical watches.

The Atmos does not have a seconds hand. All models except two do not have minute indications.

I believe that is going to difficult measuring accuracy. You can approximate something if you compare it over a long period of time, perhaps at 12 o'clock, or as much 12 o'clock as you can tell by inspecting the hands alignment.

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