I don't know if this can help, there is a question type name file response, see
this is a question type for a quiz that expects a file to be uploaded and includes an ESSAY BOX as well. You can setup your online essay assignment to an online quiz instead using this new question type (let your student ignore the uploader and use the essay box). Set up a timed quiz. Your student needs to finish within the time limit you set. I don't know if this is what you want.
Features request: time limits on assignments
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