JS: Yes. I use styles for everything in the Word document. It makes it easier. My first two steps are:
Delete everything between <style> and </style> in the html document
Find and Replace <p class="MsoNormal"> with <p>
The style sheet I import into Sigil has all the style information I used in the Word document.
There is other cleanup I do with the way I handle the Word generated TOC, Endnotes, etc. but it gives me a good starting point.
Goes pretty quickly.