>The Persians were meticulous record keepers; but no Persian source has survived
Eh, they weren't particularly big on record keeping. The Babylonians (who were part of the Persian empire) kept decent records, but not the Persians.
>Modern guesstimates by different means arrive at around 200,000.
Those are just people throwing out random figures. In reality it's highly unlikely that the Persians had the logistical capability to field an army that large beyond the fringes of their empire. Tens of thousands would likely be a more realistic number.