Wait... so for all those sketchy date estimates where it's questionable whether you even got the year right, you supposedly got them correct down to the day?
You'll have to show your work on that one
He can't.
For starters, as you allude, whether he starts with the correct year of 538 BC for the decree from Cyrus or uses the 536 BC date, he can't calculate a date, just a year.
Also, the 360 day year is arbitrary. According to Wiki, "a common Hebrew calendar year can have a length of 353, 354 or 355 days, while a leap Hebrew calendar year can have a length of 383, 384 or 385 days."
7 x 360d/y x 360y = 907200 days. Counting back from May 14, 1948 takes us into.July of 537 BC. He'd have to assume the exact date from antiquity, and he cant. In fact, if we use January of 537 BC as a starting point, we don't get out of 1947 in 907,200 days.
Then there's the matter of changing calendars. May 14, 1948 fell in the year 5708 on the Hebrew calendar. The arithmetic from the prophecy ought to yield that number.
And of course, if the numbers weren't ballpark, none of this would have been considered what would then have to have been called failed prophecy.