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To answer your question directly.

A mechanical timepiece that calls itself a marine chronometer has to be accurate to +-0.5 seconds per day.

The most accurate quartz wristwatch is certified accurate to +-5 seconds per year.

My experience, in the exact harsh real world conditions that you are talking about, is that is a realistic expectation for quartz watch to accomplish. I cant imagine why an instrument that is ~40x less precise would offer more precise timekeeping