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.