Having taken a closer look, I don't believe Anne Curry's revisionist numbers for the English, either. If the quotes posted here are correct, she accounts for men invalided home and detached to garrison Harfleur. While the size of the garrison is reasonably well attested, it's not clear how complete the surviving records of those invalided home are.
Another key missing piece is the number that died during the siege from dysentery, what the era knew as "bloody flux". The English administrative records were not set up to record a comprehensive total of deaths by disease during the siege. There is no way to get a reasonably precise number.
What we do know is that the number was high. The English lost a bishop, an earl and at least eight knights at Harfleur. The chronicler Monstrelet believed more than 2,000 died. Less than forty deaths were recorded in the official records, but so much the worse for the official records. We know that many of the records have not survived, and the death toll among the nobility and knights suggests disease deaths at about 10%.
Monstrelet's estimate might be high, or low. Given the deaths among the peerage, I wouldn't bet on 2,000 deaths being an overestimate, and many more were invalided home than died at Harfleur.
If so, the English army at Agincourt was probably closer to the 6,000 of the Gesta Henrici Quinti than the revisionist 9,000 of Anne Curry.