The command below can be faster
libreoffice --headless --convert-to pdf *.docx
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If you don't even trust the teacher to be able to open a PDF, I'd probably be more concerned about them opening the .docx file with Microsoft Office 97, or whichever archaic version they have always used on their PC, and ending up with a completely broken assignment.
Edit: Sorry I misread your comment, you talked about the process of digitally grading a PDF, I was thinking of the process of simply opening a PDF.
Not opening it, marking it up.