"It will be 0815 and Forty-Five Seconds......NOW".
Being a truckie, pre flight briefing was a far more sedate business, with each crew left to organise and brief itself, usually by each crewman giving a "departmental" account of frequencies and hence crystals required, oils and fly away kits, charts and en-route docs, role equipment etc etc. Zulu time was available in Flight Planning for individuals to set their own watches, having had the Met brief, checked Notams, filed a Flight Plan, and ordered the fuel required.
Perhaps I should have started by saying "Being a truckie based in the Far East" because on return to the UK I was posted to Colerne, just in time for the summer season of ever larger formation exercises heading towards various drop zones. The briefings for these were more like "Target for Tonight" with all the crews and the hierarchy that you recall, Danny, as audience to the various Stream Leaders, Met Men, Army Liaison, SATCOs, Sig Leaders, Nav Leaders, Eng Leaders, etc, doing their various turns. The climax, no doubt reserved to the end for its dramatic appeal, was the "Time Hack" that you described. It did not always go flawlessly. Any nervousness on the part of the "caller" would be cruelly responded to by an outbreak of "sorry, we didn't get that back here, could we have it again?", and so it would go on until the Groupie or similar would declare proceedings at an end.
A really memorable time check though was the one my nav requested at Gander Flight Planning, as the chronometer there had stopped. The clerk obliged with a "Won't be long" and disappeared into Gander Centre, which was next door. He soon re-appeared with a piece of paper on which was written "0847".