About the logic of the 72 minutes…
R Meir Posen in his sefer Or Meir has a whole kuntres about this inyan, called kuntres haneshef, and he holds 72 minutes is not uniform across the whole year in all places. It will be longer or shorter according to where you are. So in places like Gateshead, there is no RT nacht all summer long, as it never gets that dark, but there is a reddish tinge in the sky all night, in June july august.
Dayan AD Dunner told me that we are noheg the 72 minutes uniform, across the whole year and in all places. It is not based on calculations, but is just 72 minutes. That is how R’ Aharon instituted it in the US yeshivish kehillos.
According to this, sometimes it comes out BEFORE motzoei shabbos in the middle of summer in Gateshead. Obviously, the 72 mins is only lechumra.