Philspil,
I've been giving this some thought and we used to go to the Plaza fairly regularly on Wednesday and Saturday nights.
My late wife (who was my girlfriend at the time) had a birthday on November 4th, which in 1962 was on a Sunday.
I am sure from memory that the night we saw The Beatles was a weekday.
I have checked the Beatles itinerary and noticed that on Wednesday 7th November, they are recorded at visiting the Granada Studios. This would make it possible for them to do the Ritz and
the Plaza on the same day (perhaps)
As you say, there is no record of this, but, I think November 7th 1962 is favourite.