Re. your comment. That shouldn't happen. Is the version of Times New Roman that you are using a Postscript font? You might be using an old TrueType font that came with Word, or a newer TrueType font that is rendered as an Open Type font. Make sure you only have ONE version (preferably an Open Type version) of Times New Roman open and active on your machine and try the conversion again. If you can't manage that, or it still doesn't work correctly, try another oldstyle typeface such as Baskerville Old Face, Garamond, or Goudy--all three of those come with Word, so you should have them. That said, Word is not a page layout program, and it sometimes renders PDFs erratically. (I've had to use Word from time to time to layout a book, and I've found lines slipping from one page to the next, or sometimes a line at the top or bottom of a page goes missing.) So be sure to check your results carefully.
As is usually the case, you'll have to work around Word's design rather than try to make them work for you. And that's when it finally starts making sense... ...and you realize the reason you're having problems. ...and you realize the word that you need is not 'Times New Roman.