Advisor likes MS Word, I like LaTeX
In the end, once the paper is published, nobody will worry about what software was used to generate it. The software is just a means to an end.
So, if your advisor has a strong preference for Microsoft Word then - regardless how you feel about that preference - if you can't easily convince your advisor to use LaTeX you should switch to Word. There are much more important things to worry about, and there is no reason to make life difficult for your advisor for something so unimportant.
Converting your paper from LaTeX to Word is not likely to produce ideal results, as you have noticed. By the time you go through and fix things, you might as well simply work in Word from the beginning. In other words, the "efficient" way to do this is to convert the content in your head as you are writing it in Word, rather than trying to convert the content to Word after it is written.
I think you have two options:
- Learn to use Word. It may not be ideal, but this is probably not going to be the last time you are faced with a need to use it, or some similar editor.
- Offer to do all the editing. Give your professor .pdf files or printouts to comment, and then incorporate the changes yourself.
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I faced this situation the other way round when I was a PhD student. I had been using MS Office as long as it had existed. I had no trouble at all editing equations, incorporating charts from spreadsheets, formatting text etc.
My advisor preferred LaTeX, so I learned LaTeX for smoother collaboration.
For my PhD studies (in medical physics, YMMV) I used lyx as a happy medium. Lyx has a LaTeX engine but exports as Word, albeit imperfectly. In my experience one can open a LaTeX document in Lyx, spend less than ten minutes reformatting the tables, and export to a Prof as MS Word. The Prof can then mark it up with sticky notes or track changes, which can then be applied by the researcher to the original LaTeX.