I think I'm right in saying that in those days it was literally a Monday-Friday/Saturday-Sunday split. The Friday evening handover between Thames and LWT was a later change to even out the ad revenue between the two.
Pre July 68, there were no Friday night hand-overs, the weekday contractor closed down on Friday night (even if that was the small hours of Saturday morning) and the weekend one opened up on Saturday morning.
Thames/LWT from July 68 (or would it have actually been early August ?) were the first companies to perform an on air handover.
I've never been able to find out what happened on the night of the June 69 moon landing. The landing itself was around 4am on a Monday morning, and ITN's coverage continued deep into 'mid morning' I think, so when was the handover back to Thames ?