Thank you Chuck for the great support.
I'm not noticing problems anywhere apart from the Calendar, and I see that uses its own $today = getdate(); command in its template.
So, I have put your suggested code into that template, and my calpal.tmpl now reads:
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I won't know until 11pm whether that works for stopping the day changing at 11pm for me or not, the calendar is still displaying fine after that change anyway, so that is a good start.
If I've not made the correct guess re what it is best to do above forgive me, it seemed to make sense as a way forward.