I think the question is why you need to process these file at all. If the files when opened one-by-one in Word 2013 do not show up properly, no conversion process is going to help.

Word files are intended to produce documents, on paper. They will not be an accurate representation of that paper document unless opened in the same version of Word using the same operating system and printer driver. See What happens when I send my document to someone else? Will Word mess up my formatting?