Just out of curiosity, is the documentary you mention the episode of Channel 4's 'Secret History' detailing those events and first shown during 1997?
I have no specific expertise or understanding of the battle etc. but I wonder if it is pertinent that this analysis...
http://www.warship.org/no11994.htm
... makes mention of
Gneisenau having a transmitter pre-tuned to RN frequency in order to jam any outgoing signals from
Glorious.
"The Germans used a rather subtle jamming technique; instead of generating a lot of noisy interference, they attempted to drown out the legitimate signal by simultaneously generating a series of false signals which would overwhelm it, using standard RN call signs and procedures. No ship or shore station reported receiving Gneisenau's bogus messages, and in fact Devonshire was unaware that the Germans were attempting to jam Glorious' signals."
If
Glorious was aware that this method of false telegraphy could be employed (although apparently wasn't) and false messages could be misinterpreted as originating from herself, is it then not conceivable that utilising her peacetime callsign was a way of emphasising the true origin of her signals?