Should I write a different version for each program?
Yes, at least for the fit paragraph. A generic fit paragraph is worse than a short one, because it tells the committee you are applying everywhere. Send the versions together and we will read them against each other.
This comes up on Statement of Purpose Editing, where it is answered in the context of the work itself.
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Send the draft, the rubric or the score report with it. You get a real answer and a price before you commit to anything.