Hi, Your question is interesting. I do not whether I can give you a convincing answer. But I would like to point something pertaining your sentence.
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English 1b3Does using a pariticple phrase correctly express this?Yes. That's completely acceptable.
I have just started working for X today, mainly looking after the key
accounts.
English 1b3are we forced to think of the participle phrase including the perfect aspect from the main clause?No. "just start