I think I see now where the problem is. Your expectation as an instructor is correctly that successful assignment submission (or failure) should be the responsibility of the student not the marker or even the LMS. The instructional staff or the system may aid the student, but should not assume the responsibility. The document convertor should really be part of the submission process rather than feedback.
For example a better process would be
- Student is prompted to submit files in suggested formats.
- Student uploads the files
- File is converted to PDF
- Student sees that process completed correctly, resubmits new file if needed, or contacts technical support for help
- Only after PDF is converted successfully, the submission is complete and queued for the marker