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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)

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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.

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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.

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