Forgive me for butting in, but I don't think it will help. If you open your HTML file in a text editor and find one of your 'wrong' chapter headings you will see something like this if you have used the Word AllCaps styling:
Code:
<h1><span lang=EN-GB style='text-transform:uppercase'>CHaPTeR oNe</span></h1>
i.e. you will see that there are some lowercase characters in the heading. The styling
text-transform:uppercase works perfectly well when using a browser, but it is not supported by current (all???) reading devices.
If you edit your original Word doc and edit all chapter heading text to uppercase then SaveAs webpage-filtered (or your Mac equivalent) you should be fine.
My version of Word is ancient but the command to change text to uppercase is: Format - Change Case - UPPERCASE