I've recently completed my MSc in mechanical engineering and did a lot of LaTeX conversion work, so I am quite happy to execute the work for you.
Provided I get all the relevant data (e.g. images in the .docx file, all the written text, etc), I can definitely convert the document for you and provide you both the .tex file and a rendered .pdf within one day. Happy to iterate with you as well to satisfy your requirements.
Let me know when you can. Thanks.
Nick