Your right. I assumed without going back to check the Arabic that engaged was translated from Khitbah.
Why " Yazawwajanee alnabbee wa anaa bintu sitta sineen " which actually means " I became the Prophet's wife when I was a girl of six years" per what was translated "The prophet engaged me when I was a girl of six " is totally wrong. As engagement means Khitbah in Arabic which is before the Nikah.
I was wrong on this to assume what the translator rendered from the Arabic and as you know now his translation is in error. However this does not still omit the fact that Document A still contradicts Document E cause one expresses the Nikah was before the Hijrah and the other expressed the Nikah was after the Hijrah in the 2 year which still goes back to the contradiction of her age with the time line, and then on the other hadn we have a hadeeth expressing Aisha was in her puberty stage before the Hijrah while they were still in Makkah.
My point : The Prophet consumed the marriage(Nikah) when she was in her age of puberty. How old was she ? I dont know cause the hadeeths contradict other hadeeths and contradict historical timelines. Therefore I stick with Quran which was my primary source which I have done from the git go.