I was merely noting the assigned Gentile calendar date for the destruction. It's first on the Wiki list for August 4th. If an Amalekite is going to craft his own bio, he'd pick a symbolic birthdate out of the standard calendar of the nations, not one from the Jewish calendar.
Compare the Pali "Naqba" day.. it's on the 15th of May, the day after the establishment of the State of Israel (that is, the Gregorian day after the Iyar 5 of 5708/1948).
Interesting thought about possibly making up the birth date. Well, if the birth place and the parents are still subject to debate, why not the birth date as well?