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本日はお忙しいところ、ありがとうございます
A book I'm learning from translates this sentence as 'thank you for taking time out of your busy schedule today'
Is the first part a set phrase or is it just an elaborate translation? (As an aside I feel like it would make more literal sense with の rather than は)
I agree. It's an elaborate translation and it's a good way of putting it. Literally it simply says
"Today + (at a) busy time + thank you."
I also think it's a set phrase given that it's very common in emails and business correspondence.
本日は is Highlighting today's day.
Often used scenes,
'Today is the day of marriage'.
Today' is in a larger sense to thank everyone.
So the speaker says the day, Still as a short and smart way of saying is "本日は".
Meanings are "本日（のeventのために皆様）は".
Nowadays , many idioms are used in the business scene.
Because it looks like a little but overstated.