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I am curious now - at what depths is it considered human origin? Is it because we know how much the sea level has risen in the last x years?

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During the last glacial maximum 20,000 years ago the sea level was about 130 meters below today's [1] so agriculture would be found above that. About a hundred thousand years before that sea levels were close to modern levels and the current ice age [2] started almost half a million years after the first stone industry [3] got started, so sea levels would have been much higher (200-300 meters higher than today).

[1] https://en.wikipedia.org/wiki/Past_sea_level

[2] https://en.wikipedia.org/wiki/Quaternary_glaciation

[3] https://en.wikipedia.org/wiki/Oldowan

Well to be pedantic there wouldn't be any agriculture found at those depths, unless we have prehistory very, very wrong. Which is possible, and one reason why it would be good to check!

Is there any additional potential wiggle room for local uplift/erosion/etc over time, in some areas, or is that mostly a rounding error?

Yes. But 600 meters? That seems very unlikely.

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