You mentioned that "there was no evidence of any of the tippet from the dropper fly". This makes me think the 3x is not breaking, but rather the knot is slipping out of the eye. Could the knot be slipping out here?
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Some hooks are notorious for having too big of a gap here.
Could also be a sharp burr where the wire was cut during manufacture, which then cuts your dropper line when it is put under tension.